1. Pure Mathematics 1

Polynomials — Quiz

Test your understanding of polynomials with 5 practice questions.

Practice Questions

Question 1

Determine the remainder when the polynomial $f(x)=3x^3 - x^2 + 2x - 5$ is divided by $x+1$.

Question 2

Construct the monic cubic polynomial whose roots are the reciprocals of the roots of $2x^3 - 3x^2 + x - 5 = 0$.

Question 3

Use the Factor Theorem to factorise the polynomial $f(x)=x^3 + 4x^2 + x - 6$ given that $x=-2$ is a root.

Question 4

If the roots of $f(x)=ax^2+bx+c$ are $\alpha$ and $\beta$, express $\alpha^3 + \beta^3$ in terms of $a$, $b$, and $c$.

Question 5

A polynomial has a root of multiplicity 2 at $x=1$ and a simple root at $x=3$. How does its graph interact with the $x$-axis at these points?