2. Polynomial Analysis

Zeros And Roots — Quiz

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

Practice Questions

Question 1

Factor the polynomial $p(x)=3x^3-3x^2-12x+12$ completely over the real numbers. What are its real zeros?

Question 2

Find all zeros (real and complex) of $q(x)=x^2+4x+5$.

Question 3

Consider the polynomial $f(x)=(x-1)^2(x+2)^3$. Which statement correctly describes the graph’s behavior at its zeros?

Question 4

Which monic polynomial has zeros at $x=0$ (multiplicity 2) and $x=\pm\sqrt{3}$?

Question 5

For the polynomial $g(x)=(x+4)(x-1)^2(x-3)$, what is the sign of $g(x)$ on the interval $1<x<3$?