Mathovia

Math Practice

Quadratic Equations Practice Problems

Practice solving quadratic equations with the zero-product property: factor the trinomial, set each factor to zero, and read off the roots. Every equation factors over the integers and asks for the larger of its two solutions.

  1. 1.

    Solve \(x^{2} - 15x + 56 = 0\) by factoring. Enter the larger solution.

  2. 2.

    Solve \(x^{2} - 2x - 8 = 0\) by factoring. Enter the larger solution.

  3. 3.

    Solve \(x^{2} + 3x - 54 = 0\) by factoring. Enter the larger solution.

  4. 4.

    Solve \(x^{2} + x - 42 = 0\) by factoring. Enter the larger solution.

  5. 5.

    Solve \(x^{2} + 2x - 48 = 0\) by factoring. Enter the larger solution.

  6. 6.

    Solve \(x^{2} + 11x + 24 = 0\) by factoring. Enter the larger solution.

  7. 7.

    Solve \(x^{2} - 6x - 7 = 0\) by factoring. Enter the larger solution.

  8. 8.

    Solve \(x^{2} - 12x + 27 = 0\) by factoring. Enter the larger solution.

  9. 9.

    Solve \(x^{2} + 17x + 72 = 0\) by factoring. Enter the larger solution.

  10. 10.

    Solve \(x^{2} + 6x + 8 = 0\) by factoring. Enter the larger solution.
M
Written by
Mathovia Team
Editorial Team

Quadratic Equations Practice Problems

The Quadratic Equations lesson lays out all four solving methods; this practice set drills the fastest one — factoring plus the zero-product property — with instant checking. Every equation asks for the larger of its two integer solutions.

How the difficulty levels work

DifficultyWhat it drillsExample
EasyLeading coefficient , roots in
MediumLeading coefficient , roots in
HardLeading coefficient or — factor it out first

Easy and Medium drill the core loop: factor into , set each factor to zero, and take the larger root.

Hard puts a common numeric factor in front. Divide (or factor) it out first, then factor the trinomial that remains.

Using the practice problems

Choose a difficulty and a count, and the set appears. Enter the larger solution for each equation, then:

  • Check Answers grades the whole set instantly.
  • Show Answers reveals every solution for review or a key.
  • Print Worksheet builds a clean printable page.

Write both roots on paper even though you only enter one — that habit carries over to problems where both matter.

The rules these practice problems drill

RuleStatement
Standard form, one side is zero
Factor first, ,
Zero-product property or
GCF first (Hard)pull out the common numeric factor before factoring the trinomial
Two rootsevery quadratic here has two — report the larger

See the Quadratic Equations lesson for worked examples and the method-choosing guide.

Common mistakes to watch for

Applying the zero-product property when one side isn’t zero. does not give .

Dropping a root. Both factors give a solution; you just report the larger here.

Skipping the GCF at Hard. is far easier as .

Sign errors in and . A negative means opposite signs; a positive means both share the sign of .

Where to go next

To practice the factoring step on its own, use the Factoring Quadratics Practice Problems. For quadratics that do not factor, move to the Completing the Square Practice Problems and the Quadratic Formula Practice Problems. For the full picture, see the Quadratic Equations lesson.

Frequently Asked Questions

Why does the problem ask for the larger solution instead of both?+

A quadratic has two roots, and the answer box checks one number. Asking for the larger root is a reliable check that you factored correctly and applied the zero-product property, without needing to type a pair of values.

How do I enter my answer?+

Type the larger of the two solutions as a plain integer — for example 6, or -2 for a negative root. You can also write x = 6.

What is the zero-product property?+

If a product equals zero, at least one factor is zero. So means or . It only works when one side of the equation is exactly zero, which every problem here already is.

Do all of these factor over the integers?+

Yes. Every equation is built by multiplying for integer roots (at Hard, with a leading coefficient in front), so factoring always succeeds and both roots are whole numbers.

What changes at the Hard level?+

The equations gain a leading coefficient of 2 or 3, so you factor out that common number first, then factor the remaining trinomial. The roots stay integers.

What should I know before this practice set?+

Comfort factoring quadratic trinomials — try the Factoring Quadratics Practice Problems first if that is shaky — and the idea that a quadratic has up to two solutions.

More practice problems

Factoring Quadratics Practice Problems: Free Practice for Every Trinomial Type Completing the Square Practice Problems Quadratic Formula Practice Problems