$\displaystyle 24p^2 +4p - 4$
Can someone give me a step by step instruction on solving it?
sure, here you go:
Quadratic equation - Wikipedia, the free encyclopedia
Do you mean factoring it?
First factor out the common 4:
$\displaystyle 24p^2 +4p - 4 = 4(6p^2 + p - 1)$
Now turn your attention to the trinomial:
$\displaystyle 6p^2 + p - 1$
This is called the "ac" method.
Multiply the leading coefficient with the constant, in this case $\displaystyle 6 \cdot -1 = -6$
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 $\displaystyle p = (1)p = (3 - 2)p = 3p - 2p$.
So
$\displaystyle 24p^2 +4p - 4 = 4(6p^2 + p - 1)$
$\displaystyle = 4(6p^2 + 3p - 2p - 1)$
Now factor by grouping:
$\displaystyle = 4([6p^2 + 3p] + [-2p - 1])$
$\displaystyle = 4(3p~[2p + 1] + (-1)[2p + 1])$
$\displaystyle = 4(3p - 1)(2p + 1)$
-Dan