12 - The Factor Theorem, Part 1 (Factoring Polynomials in Algebra)

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In this lesson, we will learn how to factor polynomials using the factor theorem of algebra. The factor theorem says that if we know the roots of a polynomial, then we already know the factors of the same polynomial.

Also, if we know only some of the factors of the polynomial, we can use these to find the additional factors of the polynomial by doing long division or synthetic division. The higher order the polynomial, the more divisions we will need to accomplish to find all of the roots.

The factor theorem is used along with the remainder theorem in order to solve many problems involving polynomials in algebra, trigonometry, and calculus.
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My kids are musically talented and have no desire for Math and Science. Recently I have been trying to get them more excited about Math and Science and in my search for help God led me to you! Thank you Lord and thank you Jason!!! 🙌🤗 I❤️Math!

motherofpearls
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I just want to express my gratitude for these lessons. I've found my textbook and other online resources stop short at simply explaining the procedure of a mathematical concept without providing context to other lessons and the significance of why we're being taught the concept at all. Your lessons, on the other hand, are always robustly thorough and pull everything together. Thanks!

symphonyinrose
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Excellent teacher, I am 55 and skipped mathematics at school, but your explanations are brilliantly simplified, you really know your subject.

Travelingman-
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I found polynomial hard but after watching the play list, it is easy as arithmatic. I am on 12 clip I feel mor confident and everything is making sense now. I realised the rason it was hard there were gaps my knowlege of polynomial and poorly understood. I am greatful that you connected the dots and made my knowledge about the topic complete. The way you teach is fascinating anyone can follow and you dont leave gaps. I just want to say thank you.

ahmedabdulahiibrahim
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baskarv
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talhabhaiunique
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Man how can you be so smooth! I'm in 9th grade and this really helped me.

codeforyou__
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God, this made so much sense now. Please be my math teacher

rrpokedex
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I really love your explanation...I'm in grade 11 and had some issues with factor theorem.. thank you soo much!

itsmezz
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This guy helps me so much!!! Thank you so

ohmysnipesyt
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This might sound insane, but this video just fixed the issue I was having with Vandermonde determinant lol. More of a definition/language misunderstanding but it makes more sense now.

Rockyzach
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I like your lectures sir God bless you 🎉

NyamwizaLillian-qf
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Thanks very much I learned en enjoyed the lesson ....keep it up

JorimMito
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Shouldn’t the factor theorem be (bx-a) and not (x-a) alone? As we can have factors as (2x+3)(3x-7) ? B for the coffients?

hirendrall
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Isn't this just using the Remainder Theorem and seeing if the output of P(x) is 0? Therefore, the remainder is 0, and we have a factor. Correct?

jkgan
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What if one of the factors wasn’t in the shape of (x-c) as if (2x-2c) would it be factored correctly with the present of the polynomial itself and a root ……. Ex. X=-3, 3/2 are roots of f(x)=(x-3/2)(x+3)= x^2 +3x/2 - 9/2 and are also roots of g(x)= (2x-3)(x+3)=2x^2 +3x-9. Two different functions with the same exact roots how can this theorem apply to the function g(x) if we knew that one of its roots is 3/2. I am a bit confused about this theorem

FT-.
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What if we switch the signs of subtrahend to opposite signs and do additions mentally while subtracting in long division?

hemarajue
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Can I use factor theorem to find a factor of a cubic equation???

smartdean
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I'm confused how you are dividing. Can't get it.

jephphto
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