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

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.

[motherofpearls]

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[symphonyinrose]

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[Travelingman-]

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[ahmedabdulahiibrahim]

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[codeforyou__]

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[rrpokedex]

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[itsmezz]

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

[ohmysnipesyt]

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[Rockyzach]

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[NyamwizaLillian-qf]

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[JorimMito]

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[hirendrall]

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?

[jkgan]

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?

[FT-.]

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

[hemarajue]

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

[smartdean]

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

[jephphto]

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