Let f(x) = 8x3 + 16x2 − 15 and g(x) = 2x + 1. Find f of x over g of x.

A. 4 times x squared plus 6 times x minus 3 plus 12 over the quantity 2 times x plus 1

B. 4 times x squared plus 6 times x plus 3 plus 12 over the quantity 2 times x plus 1

C. 4 times x squared plus 6 times x minus 3 minus 12 over the quantity 2 times x plus 1

D. 4 times x squared plus 6 times x plus 3 minus 12 over the quantity 2 times x plus 1

4x^2 +7x-7/2

Step-by-step explanation:

f(x) = 8x3 + 16x2 − 15 and

g(x) = 2x + 1.

f of x over g of x. = f(x)/g(x)

(8x3 + 16x2 +0− 15 )/2x+1

We add 0 because we need it coefficient to stand for the coefficient of x

Using long division

4x^2 +7x-7/2

2x+1|8x^3 + 16x^2 +0 − 15

- 8x^3+4x^2

0 +14x^2+0(it drop down)

-14x^2-7x

0-7x-15(it drop down)

-(-7x)-(7/2)

-(23/2)

-15-(-7/2)

-15+7/2 = -30+7/2 = -23/2

4x^2 +7x-7/2 is the quotient remainder (-23/2)

answer: a.

step-by-step explanation: the answer is a. because, you need to converge the fractions to find a solution.