Factor the trinomial 4x^2+31x-45
To factor the trinomial 4x^2 + 31x - 45, we need to find two numbers that multiply to -180 (4 * -45) and add up to 31.
The two numbers are 36 and -5 because 36 * -5 = -180 and 36 + (-5) = 31.
Now we rewrite the middle term of the trinomial using 36x - 5x:
4x^2 + 36x - 5x - 45
Now, we group the terms and factor by grouping:
(4x^2 + 36x) + (-5x - 45)
4x(x + 9) - 5(x + 9)
(x + 9)(4x - 5)
Therefore, the factored form of 4x^2 + 31x - 45 is (x + 9)(4x - 5).