Question

How do you factor `4p ^ { 2} - 16p - 84`?

Answer 1

`4p^2-16p-84`

=`4p^2-16p+16-100`

=`(2p-4)^2-10^2`

=`(2p-4+10)*(2p-4-10)`

=`(2p+6)*(2p-14)`

Explanation:

I used difference of squares identity.

Answer 2

`4p^2-16p-84 = 4(p-7)(p+3)`

Explanation:

Given:

`4p^2-16p-84`

Note that all of the coefficients are divisible by `4`, so we can separate that out as a constant factor.

The remaining quadratic is monic (leading coefficient `1`), so we then just need to find two factors of `21` which differ by `4`. The pair `7, 3` works, so we find:

`4p^2-16p-84 = 4(p^2-4p-21)`

`color(white)(4p^2-16p-84) = 4(p-7)(p+3)`