11. Polynomial Rings

Roots And Factorization — Quiz

Test your understanding of roots and factorization with 5 practice questions.

Practice Questions

Question 1

What does it mean for $a$ to be a root of a polynomial $f(x)$?

Question 2

If $a$ is a root of $f(x)$, which factor must divide $f(x)$?

Question 3

What are the roots of $f(x)=(x-2)(x+3)$ over the real numbers?

Question 4

If $(x-5)$ is a factor of $f(x)$, what can you conclude?

Question 5

Does $f(x)=x^2+1$ have any real roots?