1. Algebra and Functions
Polynomials — Quiz
Test your understanding of polynomials with 5 practice questions.
Practice Questions
Question 1
Given that $P(x) = x^3 + ax^2 + bx + 1$ has factors $(x-1)$ and $(x+1)$, what are the values of $a$ and $b$?
Question 2
A polynomial $P(x)$ has a root at $x = 2$ with multiplicity 2 and a root at $x = -1$ with multiplicity 1. Which of the following could be the equation for $P(x)$?
Question 3
When the polynomial $P(x) = x^4 - 3x^3 + ax^2 + bx - 12$ is divided by $(x-2)$, the remainder is $0$. When divided by $(x+1)$, the remainder is $-24$. Find the values of $a$ and $b$.
Question 4
The graph of a polynomial function $f(x)$ has turning points at $x = -2$ and $x = 1$. Which of the following could be the derivative of $f(x)$?
Question 5
A polynomial $P(x)$ has a local maximum at $x = -1$ and a local minimum at $x = 3$. Which of the following statements about the graph of $P(x)$ is true?