Question

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

A.) x+2
B.) x-2
C.) x+6
D.) x-6

Answer 1

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

Factor bottom half:

`(x^(3)+3x^(2)-4x-12)/((x+3)(x+2))`

Factor top half:

`((x+3)(x^(2)-4))/((x+3)(x+2))`

Factor top (x^(2)-4) completely:

`((x+3)(x-2)(x+2))/((x+3)(x+2))`

Cancel common terms:

`((x+3)(x-2)(x+2))/((x+3)(x+2)) = ((x+3)(x-2))/((x+3)) = (x-2)`

Your quotient is x-2.