Question

What is the remainder of the quantity 4 x cubed minus 20 x minus 50 end quantity divided by the quantity x minus 3 end quantity? Show all necessary steps.

Answer 1

Explanation

We are given the following:

$\frac{4x^3-20x-50}{x-3}$

We are required to determine the remainder when the operation is carried out.

We can determine the remainder as follows:

$\begin{gathered} Let\text{ }f(x)=4x^3-20x-50 \\ Let\text{ }g(x)=x-3 \\ Suppose\text{ }g(x)=0,i.e.\text{ }x-3=0\Rightarrow x=3 \\ \\ So,f(3)=4(3)^3-20(3)-50 \\ f(3)=108-60-50=-2 \end{gathered}$

Hence, the remainder is:

$Remainder=-2$