factor the trinomial below
12x^2-11x-36
To factor the trinomial 12x^2 - 11x - 36, we need to find two numbers that multiply to -432 (the product of the leading coefficient 12 and constant term -36) and add up to the middle coefficient -11.
The two numbers that meet these criteria are -23 and 12:
-23 * 12 = -276
-23 + 12 = -11
Now, we can rewrite the middle term -11x as -23x + 12x:
12x^2 - 23x + 12x - 36
Next, we group the terms:
(12x^2 - 23x) + (12x - 36)
Now, we factor out the common factors from each group:
x(12x - 23) + 4(3x - 9)
Factored form of the trinomial: (x + 4)(12x - 9)