Practice Polynomial Functions in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

A polynomial function is formed by adding terms of the form ax^n where n is a non-negative integer. The highest power determines the degree, which controls the graph's end behavior, maximum turning points, and number of possible real zeros.

Sums of power terms with whole-number exponents. The building blocks of functions.

Example 1

easy
Find the degree and leading coefficient of p(x) = -3x^4 + 7x^2 - x + 5.

Example 2

medium
Find all zeros of p(x) = x^3 - 4x^2 + x + 6.

Example 3

medium
Perform polynomial long division: \frac{2x^3 + 3x^2 - 5x + 1}{x + 2}.

Example 4

hard
Sketch the end behavior and find all real zeros of f(x) = -2x^3 + 6x^2 + 8x. State the multiplicity of each zero.