Views: 48223
Mark Dwyer

Learn how to find all the zeros of a polynomial that cannot be easily factored. A polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The zeros of a polynomial are the values of x for which the value of the polynomial is zero.
To find the zeros of a polynomial that cannot be easily factored, we first equate the polynomial to 0. Next, we 'guess' one of the factors of the polynomial and then use synthetic division or long division to find other factor(s) the polynomial. After we have obtained the factors and have factored the polynomials, we can then use the zero-product property, quadratic formula or any other applicable property or formular to evaluate the factored polynomial and hence obtain the zeros of the polynomial.
#polynomials #zerosofpolynomials

Views: 5188
Brian McLogan

This video explains how to find all of the zeros of a degree 3 polynomial function and how to write the function as a product of linear factors.
Site: http://mathispower4u.com

Views: 38413
Mathispower4u

This video explains how to find all of the zeros of a degree 5 polynomial function and how to write the function as a product of linear factors.
Site: http://mathispower4u.com

Views: 17805
Mathispower4u

This is a topic level video of Using a Given Zero to Write a Polynomial as a Product of Linear Factors: Complex Zeros for the Global Freshman Academy College Algebra and Problem Solving Course.
Join us!
https://www.edx.org/course/college-algebra-problem-solving-asux-mat117

Views: 1521
Global Freshman Academy

http://www.freemathvideos.com In this video playlist I will show you the basics for polynomial functions. We will start with factoring polynomial equations to determine the zeros of a polynomial. We will then learn how to write the polynomial given a set of zeros. Multiplying, adding and subtracting polynomials will be apart of this series as well as classifying polynomials and determining the Leading coefficient and degree of a polynomial so that we can determine the end behavior. Next we will learn how to find all of the zeros of a polynomial using the rational zero test and descartes rule of signs. This will help us apply the factor and remainder theorem. We will also learn how to sketch the graph of a parabola using the multiplicity and zeros.
(x + 2)^3

Views: 176803
Brian McLogan

How to factorize complex polynomials. Free ebook http://bookboon.com/en/introduction-to-complex-numbers-ebook
Hi again everyone, it's Chris Tisdell here again. In this presentation I am going to continue my
series of videos on complex numbers. In previous videos we talked about complex polynomials
and how to factor them, factor theorem and we did some examples. In this video I am going to
continue on this trip with another example. So let me share my screen with you and we can
start. 00:00-00:30.
This is a reasonably long problem. We are given a polynomial which is a degree 5 polynomial.
You have got real coefficients. We are asked to do a few things asked to show that p(2i) = 0. so
2i is a root of p(z). secondly we are asked to show that z^2 +4 is a factor of the polynomial
without long division and also find the other quadratic factor and thus factorise p into linear
factors. let us just review the basic theory of complex polynomials. We have got a complex
polynomial here of degree n. there are four main parts. First of all the fundamental theorem of
algebra. Every polynomial of degree n has at least one root over the set of complex number.
That is there exists at least one number α such that p(α) = 0. 00:30-02:00.
If the coefficients of the polynomial are real then solutions appear in conjugate pairs. If α is a
root then z - α is a factor of p(z) and p(z) may be written as a product of linear factors
where the αs are the roots and the a_n are the coefficients. The first thing that we are going
to do is show that 2i is a root of a polynomial. Now this is pretty easy and I am not going to do
all the calculations for this but the critical thing to remember is that the imaginary unit 'I' satisfies
i^2 = -1. so what you will do is put 2i in 4z and we will expand this to get zero. So what does this
tell us ? This tells us that by factor theorem z - 2i is a factor of p(z). now because the
polynomial has real coefficients if we know one complex valued factor the conjugate must also
be a factor. So since the coefficients in p of z are all real, z minus the conjugate of 2i is also a
factor. The conjugate of 2i so it will be z - 2i. Alright so we have got z - 2i is factor and
z + 2i is a factor. Now remember in part b we are trying to show that z^2 +4 is a factor. If we
take this and multiply with this then this must also be a factor. So the product of this will actually
give us this. So if you expand this again remembering i^2 = -1, we see that this is also a factor.
Also we have done it without division. Also find the other quadratic factors. It says you cannot
divide up here but it does not say anything here the second bit, so that is what I am going to do.
When its divide z squared plus 4 into our polynomial and we should get something like a cubic
because this is a degree 5 and this is degree 2. Let me just fix that up real quick. 02:00-06:19.
So I forgot to write the zeros in. so we have got this 0^4, z^4 - 8 z^2 + 0 * z + 32. Let us just step by step divide this. That into that goes z^3. Okay I multiply that by each of those terms. Take this away from that so you will get
zero there. Bring this down. That will divide into -8 times. And you will get the following.
This take away from that will give you zero. Hence p(z) can be written as the following. Now
you see that this a cubic and we want to find the other factor. But this cubic is nice because it is
the difference of two cubes. 8 can be written as 2^3. So I can actually get what I am looking
for just by looking at the difference of two cubes. This is one quadratic factor and this is another
quadratic factor. You have got this linear factor here. The other quadratic factor is z^2 + 2z + 4. Okay the last thing we want to show. Factorise p(z) into complex linear factors.
Well, we have got three of those linear factors here. All of this is now splitting this up. 06:19-
09:30.
So how do you do it. You can look at the roots of this quadratic polynomial. You can apply the
quadratic formula to that and actually write down the roots. Okay you can obtain the following. it
is going to z^2 + 2z + 4 is equal to z + 1 – i√(3) and z + 1 + i √(3). I have not done all the
steps here but it is easy to do so. I can now finally write p in the factor form with linear factors.
This will go into z -2i and z + 2i. Got a z – 2 there and I can write this as the following. And there
you have it. There we have it and we have completed part c now. We were asked to factorise p
of z into linear factors. that is my presentation. Hope you enjoyed it. Hope you found it useful.
Thanks for watching this series on complex numbers. In the coming series I am going to talk
about matrices and linear system. Hope you join and hope you tune into that play list on
matrices and linear systems. If you have any suggestion or feedback leave them in the
comment below. 09:30-12:15

Views: 6305
Dr Chris Tisdell

This video introduces the Distributive Property in its general algebraic form: a(b + c) = ab + ac It shows how this patten is helpful when working with polynomials.
Part of the Algebra Basics Series:
https://www.youtube.com/watch?v=NybHckSEQBI&list=PLUPEBWbAHUszT_GebJK23JHdd_Bss1N-G
Learn More at mathantics.com
Visit http://www.mathantics.com for more Free math videos and additional subscription based content!

Views: 834900
mathantics

Views: 2933
MathwithMsPham

Sal gives numerous examples of the two special product forms: perfect squares and the difference of two squares.
Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/algebra/introduction-to-polynomials-and-factorization/special-products-of-polynomials/e/multiplying_expressions_1?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
Watch the next lesson: https://www.khanacademy.org/math/algebra/introduction-to-polynomials-and-factorization/special-products-of-polynomials/v/special-polynomials-products-1?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
Missed the previous lesson?
https://www.khanacademy.org/math/algebra/introduction-to-polynomials-and-factorization/multiplying-polynomials-by-binomials/v/multiplying-polynomials-3?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
Algebra I on Khan Academy: Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. It's also seen as a "gatekeeper" subject. Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Without it, it's impossible to move forward. It's used by people with lots of different jobs, like carpentry, engineering, and fashion design. In these tutorials, we'll cover a lot of ground. Some of the topics include linear equations, linear inequalities, linear functions, systems of equations, factoring expressions, quadratic expressions, exponents, functions, and ratios.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Algebra channel:
https://www.youtube.com/channel/UCYZrCV8PNENpJt36V0kd-4Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

Views: 323851
Khan Academy

How to use a given zero to write a polynomial as a product of linear factors - real zeros

Views: 215
larryschmidt

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Partial Fraction Decomposition - Example 5. Partial Fraction Decomposition - Example 1. In this video, I do a partial fraction decomposition where the denominator factors as a product of LINEAR and QUADRATIC factors.

Views: 386376
patrickJMT

This video introduces students to polynomials and terms.
Part of the Algebra Basics Series:
https://www.youtube.com/watch?v=NybHckSEQBI&list=PLUPEBWbAHUszT_GebJK23JHdd_Bss1N-G
Learn More at mathantics.com
Visit http://www.mathantics.com for more Free math videos and additional subscription based content!

Views: 1059093
mathantics

This algebra math video tutorial focuses on simplifying exponents with fractions, variables, and negative exponents including examples involving multiplication and division of monomials. This video discusses the basic properties of exponents and their rules such as the product rule, power rule, and quotient rule. It explains how to simplify exponential expressions with zero exponents and tells you when you add, subtract, or multiply two exponents together. This video contains plenty of examples and practice problems.
Algebra Review:
https://www.youtube.com/watch?v=cL7zrYFqdFk
How To Solve Basic Equations:
https://www.youtube.com/watch?v=Z-ZkmpQBIFo
Trigonometry Review:
https://www.youtube.com/watch?v=g8VCHoSk5_o
Epic Music Mix:
https://www.youtube.com/watch?v=qeljbZhx9bY
Excel Tutorial For Beginners:
https://www.youtube.com/watch?v=nK-uNYuvcag
Top 10 Side Hustles You Can Do To Make Extra Money:
https://www.youtube.com/watch?v=gu9YIchkmSc
How To Lose Weight Fast!
https://www.youtube.com/watch?v=cC4FUSZunsY

Views: 418598
The Organic Chemistry Tutor

The maths man presents a series of short videos on various maths topics. If there are any topics in particular that you want help with, send us an email at [email protected] and we will try and make a video on that topic. Like, comment and subscribe and tell your friends as well, and hopefully we can solve your maths problems. Check out the website www.themathsman.co.uk

Views: 56613
TheMathsMan

This video is about Adding and Subtracting Linear Expressions

Views: 30246
Anywhere Math

Polynomial Function as a Product of Linear Factors

Views: 1780
MathHelp

A http://www.door2math.com production.Write as a product of factors?
12x^2-5x-2

Views: 18678
TucsonMathDoc

This video explains how to write a matrix as a product of elementary matrices.
Site: mathispower4u.com
Blog: mathispower4u.wordpress.com

Views: 109892
Mathispower4u

This video shows you how to factor polynomials such as binomials and trinomials by removing the greatest common factor, using the ac method, substitution, and so much more. This video contains plenty of shortcut, tips, and tricks that will help you to pass your algebra class regardless if you're taking algebra 1, 2, or college algebra. This video contains tons of practice problems and examples showing you how to factor the easy way and to do it fast.
Algebra Online Course:
https://www.udemy.com/algebracourse7245/learn/v4/content
Algebra Video Playlist:
https://www.youtube.com/watch?v=i6sbjtJjJ-A&list=PL0o_zxa4K1BWKL_6lYRmEaXY6OgZWGE8G&index=1&t=13129s
Donations: https://www.patreon.com/MathScienceTutor
Here is a list of topics contain in this video:
1. Factor each polynomial completely by using the GCF or greatest common factor:
7x+21y, 8x^2y+12xy^2, 36x^3y^2-60x^4y^3
2. Factoring polynomials - difference of perfect squares
x^2-25, y^2-64, 8x^2-18, 81x^2-36y^2, 200x^4-288y^6
3. How to factor trinomials when the leading coefficient is 1 - x^2+bx+c
x^2+11x+30, x^2+2x-15, x^2-2x-48, x^2-9x+20
4. Factoring trinomials using trial and error
2x^2-5x-3
5. Factoring 3rd degree polynomials using the AC method - quadratic form - ax^2+bx+c
3x^2+5x-2, 6x^2-7x-3
6. Factoring polynomials by substitution including negative coefficients and exponents:
x^4+7x^2+12, -2x^6+6x^3+56, x^-2+13x^-1+40
7. How to factor cubic polynomials using sum and difference of perfect cubes
x^3+8, y^3-125, 27x^3+64y^6
8. Factoring polynomials expressions with 4 terms by grouping
x^3+2x2-5x-10 & 4x^3-8x^2+3x-6
9. Factoring polynomials using sum of perfect of squares (radicals)
x^2-4, x^2+4, x^2+9, x^2-3, x^2+3
10. Factoring higher degree polynomials using synthetic division and writing the answer as a product of linear factors
x^3-2x^2-5x+6 and x^4+2x^3+x^2+8x-12
11. Factoring trinomials by completing the square
x^2+6x+7, x^2-4x+12, x^2-3x+1, 2x^2+6x-9
12. Factoring advanced functions containing multiple variables
x^2-2xy+y2-9, x^2y^2-y^2-z^2+x^z^2, 5x^3+4x^2y^2+15x+12y^2

Views: 292295
The Organic Chemistry Tutor

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !!
Partial Fraction Decomposition - Example 1. In this video, I do a partial fraction decomposition where the denominator factors as a product of LINEAR factors.

Views: 889287
patrickJMT

A look at an exam question that requires a determinant to be expressed as a product of linear factors.
Factorising determinants or simplifying determinants.
AQA maths FP4

Views: 9159
Mohammed Ladak

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Example 2: https://www.youtube.com/watch?v=Sbpo2phnKxo
Finding all the Zeros of a Polynomial - Example 3. In this video, I use the rational roots test to find all possible rational roots; after finding one I use long division to factor, and then repeat! Very fun!

Views: 1078809
patrickJMT

How to express a number as the product of its prime factors. If you learnt something new and are feeling generous, please do support the channel at: https://www.patreon.com/bespokeeducation

Views: 935
BespokeEducation

Factor 4x+18 as 2(2x+9).
Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/algebra/introduction-to-polynomials-and-factorization/factoring-polynomials-1-common-factors/e/factoring-polynomials?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
Watch the next lesson: https://www.khanacademy.org/math/algebra/introduction-to-polynomials-and-factorization/factoring-polynomials-1-common-factors/v/factoring-and-the-distributive-property-2?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
Missed the previous lesson?
https://www.khanacademy.org/math/algebra/introduction-to-polynomials-and-factorization/introduction-to-factorization/v/monomial-greatest-common-factor?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
Algebra I on Khan Academy: Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. It's also seen as a "gatekeeper" subject. Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Without it, it's impossible to move forward. It's used by people with lots of different jobs, like carpentry, engineering, and fashion design. In these tutorials, we'll cover a lot of ground. Some of the topics include linear equations, linear inequalities, linear functions, systems of equations, factoring expressions, quadratic expressions, exponents, functions, and ratios.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Algebra channel:
https://www.youtube.com/channel/UCYZrCV8PNENpJt36V0kd-4Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

Views: 623684
Khan Academy

Here we write the gcd of two numbers as a linear combination. The screen became a little compact, so please pause the video as needed to follow the writing.

Views: 7930
Joshua Helston

Learn how to find all the zeros of a polynomial by grouping. A polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The zeros of a polynomial are the values of x for which the value of the polynomial is zero.
To find the zeros of a polynomial by grouping, we first equate the polynomial to 0 and then use our knowledge of factoring by grouping to factor the polynomial. Next we use the zero-product property to evaluate the factored polynomial and hence obtain the zeros of the polynomial.
Recall that the zero-product property states that when the product of two or more terms is zero, then either of the term is equal to 0.
#polynomials #zerosofpolynomials

Views: 504804
Brian McLogan

Learn how to write the equation of a polynomial when given complex zeros. Recall that a polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The zeros of a polynomial are the values of x for which the value of the polynomial is zero. Also recall that when a complex number is a zero to a polynomial, the conjugate of the complex number will also be a zero to the polynomial.
To write the equation of a polynomial, we write the given zeros in factor form and expand the product of the factors. Thus, given a, b, . . . as zeros to a polynomial, we write the equation of the polynomial by expanding the factors (x - a)(x - b) . . . = 0
#polynomials #writepolynomial

Views: 97321
Brian McLogan

By first solving the equation z^6 = -1, we see how to factorise the polynomial z^6 + 1 over the complex numbers and real numbers. Presented by Anna Tomskova from the UNSW School of Mathematics and Statistics.

Views: 7047
MathsStatsUNSW

Radical expressions can often be simplified by moving factors which are perfect roots out from under the radical sign.

Views: 758415
MyWhyU

YOUTUBE CHANNEL at https://www.youtube.com/ExamSolutions
EXAMSOLUTIONS WEBSITE at https://www.examsolutions.net/ where you will have access to all playlists covering pure maths, statistics and mechanics.
FACEBOOK: https://www.facebook.com/examsolutions.net/
TWITTER: https://twitter.com/ExamSolutions

Views: 106064
ExamSolutions

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Rational Expressions: Writing in Lowest Terms. In this example, I take two rational expressions, factor them, and cancel to write in lowest terms. I also make a remark about the domain of the two expressions obtained.

Views: 296349
patrickJMT

Prime factorization of 360 and 62. Prime factorization which is also called integer factorization or prime decomposition involves finding which numbers multiply together to equal the original number. In this video, I use a factor tree to find the prime factors of 360 and 62.
In this video, I will express as a product of its prime numbers
Integer factorization of 360
Integers factorization of 62
Prime decomposition of 360
Prime factorization of 62
Which numbers multiply together to equal 360
Which numbers multiply together to equal 62
Set of prime numbers for 360
List of prime numbers for 62
MooMooMath and Science upload a new math or science video every day. We have over 1400 math and science videos to help in school and life.
https://www.youtube.com/channel/UCE_WiQFez8FZcICpbwblyyg

Views: 97
MooMoo Math and Science

Learn how to write the equation of a polynomial when given complex zeros. Recall that a polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The zeros of a polynomial are the values of x for which the value of the polynomial is zero. Also recall that when a complex number is a zero to a polynomial, the conjugate of the complex number will also be a zero to the polynomial.
To write the equation of a polynomial, we write the given zeros in factor form and expand the product of the factors. Thus, given a, b, . . . as zeros to a polynomial, we write the equation of the polynomial by expanding the factors (x - a)(x - b) . . . = 0
#polynomials #writepolynomial

Views: 2560
Brian McLogan

Section 11a from Math 1101

Views: 26324
Bauman

In this lesson by Venkata Raghulan (CAT 99.99%iler) you will learn an interesting concept from Number Systems for CAT - the number of ways in which you can express a number as a product of 2 factors.

Views: 803
Magnus Prep

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! The Conjugate Pair Theorem - Example 2. In this video, I factor a 3rd degree polynomial completely given one known complex root.

Views: 142403
patrickJMT

Made with Explain Everything

Views: 640
AHMathis1

Simplifying Rational Expressions
Watch the next lesson: https://www.khanacademy.org/math/algebra2/polynomial_and_rational/simplifying-rational-expressions/v/simplifying-rational-expressions-1?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII
Missed the previous lesson?
https://www.khanacademy.org/math/algebra2/polynomial_and_rational/binomial_theorem/v/binomial-theorem-part-3?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII
Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Algebra II channel:
https://www.youtube.com/channel/UCsCA3_VozRtgUT7wWC1uZDg?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

Views: 1591045
Khan Academy

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !!
Solving Quadratic Inequalities
The basic procedure and one full example is shown!
For more free math videos, visit http://PatrickJMT.com

Views: 867208
patrickJMT