Question

Create a factorable polynomial with a GCF of 5z. Rewrite that polynomial in two other equivalent forms. Explain how each form was created. (10 points)

Answer 1

Lets assume a polynomial

$5zx^2 + 25zx +30z$

Here GCF is 5z

all terms are divisible by 5z. so greatest common factor is 5z

$5zx^2 + 25zx +30z$

One form of polynomial is $5z (x^2 + 5x +6)$

We factor the polynomial further

Other form of polynomial is $5z(x+3)(x+2)$

$5z (x^2 + 5x +6)$  and $5z(x+3)(x+2)$ are the two forms of polynomial $5zx^2 + 25zx +30z$

First form $5z (x^2 + 5x +6)$  is created by taking out GCF 5z

SEcond form $5z(x+3)(x+2)$  is created by factoring x^2 + 5x + 6