Free Printable WorksheetMathAlgebra IMath CurriculumA-REI.4a–b

ALG1.88 Solve Quadratic Equations by Factoring Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra I Math worksheet provides structured practice on ALG1.88 Solve Quadratic Equations by Factoring. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG1.88 Solve Quadratic Equations by Factoring - Select the correct solution to quadratic equations by factoring and applying the zero product property; Select the check that verifies solutions and interpret them as zeros or x-intercepts when appropriate. (CCSS: A-REI.4a–b; TEKS: §111.39(c)(6)(A–C); VA SOL: A.EI.3 a–c; FL B.E.S.T.: MA.912.AR.3.1, 3.8; NY-NGLS: AI-A.REI.4a–b; CA CCSSM: A-REI.4; MA 2017: HS.A-REI.4; DoDEA CCRSM; NAEP: Algebra—equations; NCTM P2A: Practices 1, 6.)

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Algebra I

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related ALG1.88 Solve Quadratic Equations by Factoring skill assessments:

Problem 1Difficulty: Mastery
A model for height uses h(t) = -0.5(t - 6)(t + 10), where t is time in seconds and t >= 0. Which answer correctly solves h(t) = 0 and interprets the result?
AThe only algebraic root is t = 6 because negative factors are ignored.
BThere are no roots because the coefficient is negative.
CThe algebraic roots are t = 6 and t = -10; only t = 6 seconds is meaningful in the time context.
DThe algebraic roots are t = -6 and t = 10; only t = 10 seconds is meaningful in the time context.
Solution & Explanation:Set each factor equal to zero: t - 6 = 0 gives t = 6, and t + 10 = 0 gives t = -10. Since time is restricted to t >= 0, only 6 seconds is meaningful.
Problem 2Difficulty: Mastery
A factoring card shows (4x - 3)(x + 2) = 0. Which expanded equation and solution set match the card?
A4x2 - 5x - 6 = 0; x = -3/4 or x = 2
B4x2 + 11x + 6 = 0; x = -3/4 or x = -2
C4x2 - 11x + 6 = 0; x = 3/4 or x = 2
D4x2 + 5x - 6 = 0; x = 3/4 or x = -2
Solution & Explanation:Expanding gives 4x2 + 8x - 3x - 6 = 4x2 + 5x - 6. The factors give x = 3/4 or x = -2.
Problem 3Difficulty: Mastery
Solve 2x2 + 4x - 30 = 0.
Ax = 15 or x = -1
Bx = 5 or x = -3
Cx = -5 or x = 3
Dx = -15 or x = 1
Solution & Explanation:Factor out 2 to get 2(x2 + 2x - 15) = 0. Then x2 + 2x - 15 = (x + 5)(x - 3), so x = -5 or x = 3.

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Frequently Asked Questions

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Algebra I Math students. It aligns with educational standard A-REI.4a–b (Primary standard selected for prompt fields in this prompt cell: CCSS A-REI.4a–b. Skill statement in this prompt cell: Select the correct solution to quadratic equations by factoring and applying the zero product property; Select the check that verifies solutions and interpret them as zeros or x-intercepts when appropriate. Associated standards listed with this skill in the curriculum source: CCSS: A-REI.4a–b; TEKS: §111.39(c)(6)(A–C); VA SOL: A.EI.3 a–c; FL B.E.S.T.: MA.912.AR.3.1, 3.8; NY-NGLS: AI-A.REI.4a–b; CA CCSSM: A-REI.4; MA 2017: HS.A-REI.4; DoDEA CCRSM; NAEP: Algebra—equations; NCTM P2A: Practices 1, 6. Use this prompt-provided wording as the supporting standard description for this workflow.).

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