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

Answer:NOT A.

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)