1.Find the real roots of the quadratic equation by factoring: x² - 5x - 24 = 0
Ax = -8 and x = 3
Bx = 8 and x = -3
Cx = 6 and x = -4
Dx = -6 and x = 4
Working
Grade 9algebraOriginal practice
Algebra 1: Solving Quadratic Equations & The Quadratic Formula
Master factoring trinomials, evaluating the discriminant, and applying the quadratic formula with complete worked step-by-step solutions.
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About this practice
Grade 9 · math · Matching answer key included · US Letter and A4
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Teaching guide, sample answers and curriculum references
Before you begin
Expand and factor simple expressions and understand an equation's solutions.
How to use this worksheet
- Model the target skill: solve quadratic equations ax² + bx + c = 0 by factoring and zero-product property. Use the first task as a guided example before asking for an independent response.
- Check readiness first: Expand and factor simple expressions and understand an equation's solutions.
- Discuss an incorrect response using this distinction: Setting each factor to zero is valid when their product equals zero; a nonzero right side requires another step.
A common mistake to discuss
Setting each factor to zero is valid when their product equals zero; a nonzero right side requires another step.
What to practice next
Substitute both proposed roots into the original equation.
Sample question and answer
Find the real roots of the quadratic equation by factoring: x² - 5x - 24 = 0
- A. x = -8 and x = 3
- B. x = 8 and x = -3
- C. x = 6 and x = -4
- D. x = -6 and x = 4
Answer: B. Look for two numbers that multiply to -24 and add to -5. The factors are -8 and 3: (x - 8)(x + 3) = 0. Setting each factor to zero gives x = 8 or x = -3.
Intended curriculum references: CCSS.MATH.CONTENT.HSA.REI.B.4 · CCSS.MATH.CONTENT.HSA.REI.B.4.B. These references describe learning goals; they are not endorsements.
Published 2026-10-02; updated 2026-10-02. Original MakeWorksheet practice. Automated consistency checks support publication; independent subject-specialist review is not recorded. Read our editorial policy.
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