Chapter 4.4, Problem 6MCQ

To determine

To find: The remainder for $\left(x^3-4x^2+2x-6\right)÷\left(x-4\right)$ using the Remainder Theorem.

Answer to Problem 6MCQ

After divide we get a remainder of 2, this gives us $x^2+2+\frac{2}{x-4}$

Explanation of Solution

Given information: $\left(x^3-4x^2+2x-6\right)÷\left(x-4\right)$

Calculation:

  

When you divide you get a remainder of 2. This gives us:

  $\frac{x^3-4x^2+2x-6}{x-4}=x^2+2+\frac{2}{x-4}$