Re: Factoring a polynomial

Reneg

continue the factorization process. and factorize the (x^3-1) it will give you (x-1)(x^2+x+1). therefore the polynomial after factorization becomes

(x^2+2)(x-1)(x^2+x+1).

now how to factorize the x^3-1 ..the (x-1) is a factor of the polynomial x^3 -1 therefore dividing by (x-1) or simply use Horner's method

(Horner's method - Wikipedia, the free encyclopedia ) you will get the result .

MINOAS

Re: Factoring a polynomial

I just don't see how you can factor out $\displaystyle x - 1$ from $\displaystyle (x^3 - 1)(x^2 + 2)$ because there is no greatest common factor other than 1

Re: Factoring a polynomial

Quote:

Originally Posted by

**ReneG** I just don't see how you can factor out $\displaystyle x - 1$ from $\displaystyle (x^3 - 1)(x^2 + 2)$ because there is no greatest common factor other than 1

$\displaystyle (x^3-1)=(x-1)(x^2+x+1)$ the difference of two cubes.

Re: Factoring a polynomial

Do you know how to **multiply** polynomials? What do you get when multiply $\displaystyle (x- 1)(x^2+ x+ 1)$?

Re: Factoring a polynomial

Oh wow, completely forgot about that rule. Seeing 1 as a cube root of 1 wasn't really intuitive for me at first, thanks!