Free Printable WorksheetMathAlgebra IIMath CurriculumA-REI.11–12

ALG2.114 Polynomial Inequalities Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra II Math worksheet provides structured practice on ALG2.114 Polynomial Inequalities. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG2.114 Polynomial Inequalities - Primary standard selected for prompt fields in this prompt cell: CCSS A-REI.11–12. Skill statement in this prompt cell: Select the correct solution(s) to polynomial inequalities using sign charts and interval testing, and connect solutions to graph regions. Associated standards listed with this skill in this prompt cell: CCSS A-REI.11–12; CA CCSSM A-REI.11–12; MA 2017 A-REI.11–12; NY NGLS A-REI.11–12; TX TEKS Algebra II: §111.40. Use this prompt-provided wording as the supporting standard description for this workflow.

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 II

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 ALG2.114 Polynomial Inequalities skill assessments:

Problem 1Difficulty: Mastery
A polynomial has zeros at -4, -2, 1, and 5. The zero at x = -2 has even multiplicity, all other listed zeros have odd multiplicity, and the leading coefficient is negative. Which set solves p(x) >= 0?
A(-inf, -4] U [1, 5]
B[-4, -2] U [1, 5]
C(-inf, -4] U {-2} U [1, 5]
D[-2, 1] U [5, inf)
Solution & Explanation:A negative leading coefficient makes the polynomial negative for large positive x. Moving left, the sign changes at 5 and 1, stays the same at the even zero -2, and changes at -4. Include the zeros because the inequality is >= 0.
Problem 2Difficulty: Mastery
A polynomial has zeros at -3, 2, and 6. The zero at x = 2 has even multiplicity, and the leading coefficient is positive. Which set solves p(x) < 0?
A(-inf, -3) U (6, inf)
B(-3, 2) U (2, 6)
C(-3, 6)
D[-3, 2] U [2, 6]
Solution & Explanation:With positive leading coefficient, the graph is above for large positive x. The sign changes at odd-multiplicity zeros -3 and 6, but not at the even-multiplicity zero 2. Strictly negative intervals are (-3, 2) and (2, 6).
Problem 3Difficulty: Mastery
Let p(x) = a(x + 4)2(x - 1)(x - 6), where a > 0. Which set solves p(x) <= 0?
A[1, 6]
B{-4} U [1, 6]
C(-inf, -4] U [1, 6]
D[-4, 1] U [6, inf)
Solution & Explanation:The positive constant a does not change the sign. The squared factor gives an isolated zero at -4, and (x - 1)(x - 6) is nonpositive from 1 to 6, so the solution is {-4} U [1, 6].

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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 II Math students. It aligns with educational standard A-REI.11–12 (Primary standard selected for prompt fields in this prompt cell: CCSS A-REI.11–12. Skill statement in this prompt cell: Select the correct solution(s) to polynomial inequalities using sign charts and interval testing, and connect solutions to graph regions. Associated standards listed with this skill in this prompt cell: CCSS A-REI.11–12; CA CCSSM A-REI.11–12; MA 2017 A-REI.11–12; NY NGLS A-REI.11–12; TX TEKS Algebra II: §111.40. Use this prompt-provided wording as the supporting standard description for this workflow.).

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