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* 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)`.