Thread: four term polynomial with gcf

1. four term polynomial with gcf

Hi all;
I need to factor 16x^3y^3 +16 - 8y^3 - 32x^3 which is a four term polynomial with a common factor of 8, giving 8(2x^3y^3 +2 -y^3 - 4x^3) rearranging the poly in the brackets so they can be grouped gives 2x^3y^3 - y^3 - 4x^3 +2.

Which gives a factored version of (8y^3 - 16)(2x^3 - 1).

But if I rearranged the polynomial differently 2x^3y^3 - y^3 + 2 - 4x^3

I end up with 8y^3(2x^3 - 1) + 16(1 - 2x^3) the binomials are different why?

Thanks.

2. Originally Posted by anthonye
Hi all;
I need to factor 16x^3y^3 +16 - 8y^3 - 32x^3 which is a four term polynomial with a common factor of 8, giving 8(2x^3y^3 +2 -y^3 - 4x^3) rearranging the poly in the brackets so they can be grouped gives 2x^3y^3 - y^3 - 4x^3 +2.

Which gives a factored version of (8y^3 - 16)(2x^3 - 1).

But if I rearranged the polynomial differently 2x^3y^3 - y^3 + 2 - 4x^3

I end up with 8y^3(2x^3 - 1) + 16(1 - 2x^3) the binomials are different why?

Thanks.

$\displaystyle 8y^3(2x^3 - 1) + 16(1 - 2x^3) = 8y^3(2x^3 - 1) - 16(2x^3 - 1) = (2x^3 - 1)(8y^3 - 16)$

3. Ok I see what you did but more explanation please.

4. Originally Posted by anthonye
Ok I see what you did but more explanation please.
what's to explain? the two expressions that you said are "different" are the same.

5. Yeah I see now, Also in a four term polynomial you dont have to take out the common factor before grouping do you and can the grouping method be applied to all even term polynomials.