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 Polynomials and factoring

Example 4 from Algebra and Trigonometry, 5.3 Graphs of Polynomial Functions

Finding the y- and x-Intercepts of a Polynomial in Factored Form

Find the y- and x-intercepts of $g (x) = {(x - 2)}^{2} (2 x + 3) .$

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
The y-intercept can be found by evaluating $g (0) .$

$\begin{matrix} g (0) & = & {(0 - 2)}^{2} (2 (0) + 3) \\ = & 12 \end{matrix}$

So the y-intercept is $(0, 12) .$

The x-intercepts can be found by solving $g (x) = 0.$

${(x - 2)}^{2} (2 x + 3) = 0$

$\begin{matrix} {(x - 2)}^{2} & = & 0 & (2 x + 3) & = & 0 \\ x - 2 & = & 0 & or & x & = & - \frac{3}{2} \\ x & = & 2 \end{matrix}$
So the x-intercepts are $(2, 0)$ and $(- \frac{3}{2}, 0) .$

How did it go?

PreviousFinding the x-Intercepts of a Polynomial Function by Factoring Next Finding the x-Intercepts of a Polynomial Function Using a Graph

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 5.3, 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.