Please help solve 12x^3-48x^2-75x-24/6x+3

Question

I really need help solving this.  Could you please show the work so that I understand what i am doing.  Thank you very much everyone.

Answer 1

I read this as (12x^3-48x^2-75x-24)/(6x+3). Divide top and bottom by 6: 2x^3-8x^2-12.5x-4)/(x+1/2).

We can use synthetic division:

-1/2 | 2 -8 -12.5 -4

.........2 -1....4.5..4

.........2 -9......-8 | 0 = 2x^2-9x-8

Provided x≠-1/2 the quotient is 2x^2-9x-8 which is a simplification of the original expression.