Question

What the remainder when f(x)=x^3+5x^2-32x-7 is divided by x-4? Show all the steps

Answer 1

We need to find the remainder of the division of:

`f\mleft(x\mright)=x^3+5x^2-32x-7`

by x -4.

According to the Remainder Theorem, the remainder of the division of f(x) by x - a is f(a).

In this problem, a = 4. Thus, the remainder of this division is:

`\begin{gathered} f(4)=4^3+5(4)^2-32(4)-7 \\ \\ =64+80-128-7 \\ \\ =9 \end{gathered}`

Therefore, the remainder when f(x) is divided by x - 4 is 9.

Answer: 9