11. Polynomial Rings

Division Algorithm — Quiz

Test your understanding of division algorithm with 5 practice questions.

Practice Questions

Question 1

When $2x^3+3x^2-5x+6$ is divided by $x+2$, what is the remainder?

Question 2

If $f(x)=x^3-4x+1$, what is the remainder when $f(x)$ is divided by $x-1$?

Question 3

In the division algorithm $f(x)=g(x)q(x)+r(x)$, which condition must the remainder $r(x)$ satisfy?

Question 4

What is the quotient when $x^2+5x+6$ is divided by $x+2$?

Question 5

What is the remainder when $x^2+1$ is divided by $x^3-2x+1$?