Answer:
The quotient is x -2
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