Question

An expression is shown below: 3pf2 − 21p2f + 6pf − 42p2 Part A: Rewrite the expression so the GCF is factored completely.

Answer 1

Given:

The expression is:

$3pf^2-21p^2f+6pf-42p^2$

To find:

The factored form of the given expression by taking out the GCF.

Solution:

We have,

$3pf^2-21p^2f+6pf-42p^2$

In the given expression the terms are $3pf^2,-21p^2f,6pf,-42p^2$. The common factors are $3,p$.

$GCF=3\times p$

$GCF=3p$

Taking out the GCF from the given expression, we get

$=3p(f^2-7pf+2f-14p)$

After the complete factor, we get

$=3p(f(f-7p)+2(f-7p))$

$=3p(f-7p)(f+2)$

Therefore, the factored form after taking out the GCF is $3p(f^2-7pf+2f-14p)$ and the complete factored form is $3p(f-7p)(f+2)$.