# Thread: Easy factoring homework help

1. ## Easy factoring homework help

$24p^2 +4p - 4$

Can someone give me a step by step instruction on solving it?

2. Originally Posted by nerdzor
$24p^2 +4p - 4$

Can someone give me a step by step instruction on solving it?
$(12p-4)(2p+1)$

3. Originally Posted by nerdzor
$24p^2 +4p - 4$

Can someone give me a step by step instruction on solving it?
Do you mean factoring it?

First factor out the common 4:
$24p^2 +4p - 4 = 4(6p^2 + p - 1)$

Now turn your attention to the trinomial:
$6p^2 + p - 1$

This is called the "ac" method.

Multiply the leading coefficient with the constant, in this case $6 \cdot -1 = -6$

Now form a list of the pairs of factors of -6:
1, -6
2, -3
3, -2
6, -1

Now compare the sum of each pair of factors with the coefficient of the linear term of the quadratic, in this case 1. I get that 3 + (-2) = 1. So we want to write the linear term of the quadratic as $p = (1)p = (3 - 2)p = 3p - 2p$.

So
$24p^2 +4p - 4 = 4(6p^2 + p - 1)$

$= 4(6p^2 + 3p - 2p - 1)$

Now factor by grouping:
$= 4([6p^2 + 3p] + [-2p - 1])$

$= 4(3p~[2p + 1] + (-1)[2p + 1])$

$= 4(3p - 1)(2p + 1)$

-Dan