Question

Let f(x) = -3x3 + 4 and g(x) = -8x2 + 2x. What is f(x) · g(x)?

Answer 1

We are given the following functions

$\begin{gathered} f(x)=-3x^3+4 \\ g(x)=-8x^2+2x \end{gathered}$

Let us find the product of the two functions.

$\begin{gathered} f(x)\cdot g(x)=(-3x^3+4)\cdot(-8x^2+2x) \\ f(x)\cdot g(x)=(-3x^3\cdot-8x^2)+(-3x^3\cdot2x)+(4\cdot-8x^2)+(4\cdot2x) \\ f(x)\cdot g(x)=(24x^{3+2})+(-6x^{3+1})+(-32x^2)+(8x) \\ f(x)\cdot g(x)=(24x^5)+(-6x^4)+(-32x^2)+(8x) \\ f(x)\cdot g(x)=24x^5-6x^4-32x^2+8x \end{gathered}$

Therefore, the product of the functions f(x) and g(x) is

$24x^5-6x^4-32x^2+8x$

The 1st option is the correct answer.