what is the quotient of $(x^{3}+3x^{2}-4x - 12)div(x^{2}+5x + 6)$?

Explanation:

Step1: Factor the numerator

Factor (x^{3}+3x^{2}-4x - 12) by grouping. (x^{2}(x + 3)-4(x + 3)=(x + 3)(x^{2}-4)=(x + 3)(x + 2)(x-2))

Step2: Factor the denominator

Factor (x^{2}+5x + 6). We find two numbers that multiply to (6) and add to (5), which are (2) and (3). So (x^{2}+5x + 6=(x + 2)(x+3))

Step3: Calculate the quotient

(\frac{(x + 3)(x + 2)(x-2)}{(x + 2)(x + 3)}=x-2)

Answer:

(x - 2)