What is the quotient of (x^3+3x^2-4x-12) / (x^2+5x+6) ?

The quotient is x - 2

Step-by-step explanation:

1. Let's simplify and find out the quotient of the following division:

(x^3+3x^2-4x-12) / (x^2+5x+6)

(x³ + 3x² - 4x - 12) / (x² + 5x + 6)

(x + 2) (x² + x - 6) / (x + 2) (x + 3) ⇒ Factorizing on the numerator and the denominator

(x² + x - 6) / (x + 3) ⇒ Eliminating (x + 2) on the numerator and the denominator

(x + 3) (x - 2) / (x + 3) ⇒ Factorizing on the numerator

x - 2 ⇒ Eliminating (x + 3) on the numerator and the denominator

The quotient is x - 2