Skip to content

Physics Playground

Simulations How we teach Pricing

Language

Log in Start learning free

Loading…

Physics Playground

Built on open, peer-reviewed sources: OpenStax, The Feynman Lectures on Physics, HyperPhysics, NASA and NIST. See our sources.

Learn

Physics course
Math for Physics
Start with the math toolkit
Simulations
Glossary
Exercises
Past exams
Library
How we teach

Company

Pricing
Terms
Privacy
Contact

© 2026 Physics Playground. Made for the curious.Language

Exercises Equations and inequalities

Example 4 from Algebra and Trigonometry, 2.6 Other Types of Equations

Solving a Polynomial by Factoring

Solve the polynomial by factoring: $5 x^{4} = 80 x^{2} .$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
First, set the equation equal to zero. Then factor out what is common to both terms, the GCF.

$\begin{matrix} 5 x^{4} - 80 x^{2} & = & 0 \\ 5 x^{2} (x^{2} - 16) & = & 0 \end{matrix}$
Notice that we have the difference of squares in the factor $x^{2} - 16,$ which we will continue to factor and obtain two solutions. The first term, $5 x^{2},$ generates, technically, two solutions as the exponent is 2, but they are the same solution.

$\begin{matrix} 5 x^{2} & = & 0 \\ x & = & 0 \\ x^{2} - 16 & = & 0 \\ (x - 4) (x + 4) & = & 0 \\ x & = & 4 \\ x & = & −4 \end{matrix}$
The solutions are $0 (double solution),$ $4,$ and $−4.$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Solve by factoring: $12 x^{4} = 3 x^{2} .$

How did it go?

PreviousSolving an Equation Involving Rational Exponents and Factoring Next Solve a Polynomial by Grouping

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 2.6, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.