Question

What is the f of x over the g of x when f(x) = − 2x3 + x2 + 16x − 15 and g(x) = x + 3?

−2x2 − 5x + 1
− 2x2 + 7x − 5
−2x2 + 7x − 5 − 12 over the quantity of x plus 3
− 2x2 − 5x + 1 − 12 over the quantity of x plus 3

Answer 1

f(x) = − 2x3 + x2 + 16x − 15 and g(x) = x + 3$\frac{f(x)}{g(x)}= \frac{-2x^3 +x^2 +16x -15}{x+3}$

We can use synthetic division to divide it

x+3=0 or x=-3

So

-3__ |____-2 ____ 1 ____ 16 ____ -15

___ | _________6 ____-21 ____15

______________________

_______ -2____7____ -5 ____0

So the expressions should be $-2x^2 +7x -5$

That is Option B