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

2 Answers
Jul 18, 2017

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.

Jul 18, 2017

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)