Factor by grouping.
6p^2-17p-45
To factor by grouping, we need to break down the middle term (-17p) into two terms whose coefficients multiply to give us the product of the square term coefficient (6) and the constant term (-45).
The coefficients of the two terms must be factors of 6 and -45 that add up to -17.
The factors of 6 are 1, 2, 3, and 6. The factors of -45 are 1, 3, 5, 9, 15, and 45.
After checking the possibilities, we find that the factors that add up to -17 are 3 and -15.
So we rewrite the middle term as -15p + 3p:
6p^2 - 17p - 45 = 6p^2 - 15p + 3p - 45
Now, we can group the first two terms and the last two terms together:
(6p^2 - 15p) + (3p - 45)
Next, we factor out the greatest common factor from each group:
3p(2p - 5) + 3(2p - 15)
Notice that there is a common binomial factor of (2p - 5) in both groups. We can now factor it out:
(2p - 5)(3p + 3)
Therefore, the factored form of 6p^2 - 17p - 45 is (2p - 5)(3p + 3).