Polynomial Functions

End behaviour, zeros and multiplicity, the remainder and factor theorems, and matching equations to graphs.

10 questions, free, marked as you go with a worked explanation on every one.

What this covers

What is the end behaviour of y = −2x³ + 5x − 1?
How does the graph of y = (x − 1)²(x + 3) behave at x = 1?
What is the remainder when P(x) = x³ − 4x² + 2x + 5 is divided by x − 3?
Which of these is a factor of P(x) = x³ − 2x² − 5x + 6?
Use synthetic division to divide 2x³ + 3x² − 5x + 6 by x + 2. What is the remainder?
Which equation matches the graph shown?
How many distinct real zeros does the polynomial function graphed have?
A polynomial function crosses the x-axis at x = −2 and x = 4 and touches it at x = 1. What is its least possible degree?
What are the zeros of P(x) = x³ − 7x + 6?
When x³ + kx² − 4x + 3 is divided by x − 2, the remainder is 15. What is the value of k?