Factor by grouping.
64p^2 - 48p - 27
To factor by grouping, we need to break up the middle term (-48p) into two terms that can be factored out separately.
64p^2 - 48p - 27
First, let's find the factors of 64 and -27:
64: 1, 2, 4, 8, 16, 32, 64
-27: 1, -1, 3, -3, 9, -9, 27, -27
Looking at the factors, we can see that -3 and 9 when added together give us -48. So we can rewrite the middle term as:
64p^2 - 3p + 9p - 27
Now, we can factor by grouping:
= 16p(4p - 3) + 3(4p - 3)
= (16p + 3)(4p - 3)
Therefore, the factored form of 64p^2 - 48p - 27 is (16p + 3)(4p - 3).