Question

6(2p+q)^2-5(2p+q)-25

Answer 1

6(2p+q)^2 - 5(2p+q) - 25
Let t = (2p+q). Then, the above expression becomes:
6t^2 - 5t - 25
Use the AC method to factor:
a = 6, b = -5, c = -25
a * c = 6 * (-25) = -150.
What two numbers multiply to -150 and add to -5?
-15 and 10
6t^2 - 5t - 25 =
6t^2 - 15t + 10t - 25 =
3t(2t - 5) + 5(2t - 5) =
(2t - 5)(3t + 5)
Replace t by (2p+q)
( 2(2p+q) - 5 ) * ( 3(2p+q) + 5 ) =
(4p + 2q - 5)(6p + 3q + 5)