Question

Janis divided the two polynomials shown

8 x ^ 2 - 10 x - 12 / 4x + 3.
What is the Quotient?


A. 2x + 4
B. 2x - 1 + -9 / 4x + 3
C. 2x - 4
D. 2x - 1 + -15 / 4x + 3

Answer 1

Choice C is the correct answer

Explanation:

The first step is to factorize the numerator;

`8x^(2) -10x-12`

We need to determine two numbers such that their sum is -10 and their product 8(-12) = -96. The two numbers by trial and error are -16 and 6. Consequently, we substitute the middle term in the expression by these two numbers;

`8x^(2)-16x+6x-12`

Upon simplification this becomes;

`8x(x-2)+6(x-2)\\2(4x+3)(x-2)`

Dividing by the denominator the common terms 4x+3 cancel each other and the quotient thus becomes;

2x-4