Free Printable WorksheetMathAlgebra IMath CurriculumA-APR.1 (coherence)

ALG1.79 Divide Polynomials by Monomials Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra I Math worksheet provides structured practice on ALG1.79 Divide Polynomials by Monomials. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG1.79 Divide Polynomials by Monomials - Select the correct quotient for polynomials by monomials and simplify expressions; Identify domain restrictions when division introduces excluded values. (CCSS: A-APR.1 (coherence); TEKS: §111.39(c)(10)(C)–(D); VA SOL: A.EO.2 d; FL B.E.S.T.: MA.912.AR.1.4; NY-NGLS: AI-A.SSE.2 (rewriting) connections; CA CCSSM: A-APR connections; MA 2017: HS.A-APR.1 (course model dependent); DoDEA CCRSM; NAEP: Algebra—symbolic manipulation; NCTM P2A: Practices 6, 7.)

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 ALG1.79 Divide Polynomials by Monomials skill assessments:

Problem 1Difficulty: Mastery
Which rule is the best general description for dividing a polynomial by a monomial cxk when k > 0 and each numerator term has at least xk?
ADivide each term by cxk, subtract exponents of x, and keep x != 0 as an original-domain restriction
BAdd k to each exponent because division makes powers larger
CAfter simplifying to a polynomial, remove all original-domain restrictions
DDivide only the leading term by c and ignore xk
Solution & Explanation:A monomial divisor applies to every term. For powers of x, division subtracts exponents, and because cxk is 0 at x = 0 when k > 0, x != 0 remains an original-domain restriction.
Problem 2Difficulty: Mastery
Simplify (-12x4 + 9x3 - 6x2) / (-3x2), and include the restriction.
A4x2 - 3x + 2, x != 0
B-4x2 + 3x - 2, x != 0
C4x2 + 3x + 2, x != 0
D4x2 - 3x + 2, no restriction
Solution & Explanation:Each term is divided by -3x2: -12x4/(-3x2) = 4x2, 9x3/(-3x2) = -3x, and -6x2/(-3x2) = 2. The divisor gives x != 0.
Problem 3Difficulty: Mastery
Let g(x) = (24x5 - 18x4 + 6x3) / (6x3) - (2x2 - x). What is g(x) with the original restriction?
A2x2 - 2x + 1, x != 0
B2x2 - 2x + 1, no restriction
C2x2 - 4x + 1, x != 0
D4x2 - 3x + 1, x != 0
Solution & Explanation:First divide the polynomial by 6x3 to get 4x2 - 3x + 1. Subtracting 2x2 - x gives 2x2 - 2x + 1. The original quotient has x3 in the denominator, so x != 0.

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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-APR.1 (coherence) (Primary standard selected for prompt fields in this prompt cell: CCSS A-APR.1 (coherence). Skill statement in this prompt cell: Select the correct quotient for polynomials by monomials and simplify expressions; Identify domain restrictions when division introduces excluded values. Associated standards listed with this skill in the curriculum source: CCSS: A-APR.1 (coherence); TEKS: §111.39(c)(10)(C)–(D); VA SOL: A.EO.2 d; FL B.E.S.T.: MA.912.AR.1.4; NY-NGLS: AI-A.SSE.2 (rewriting) connections; CA CCSSM: A-APR connections; MA 2017: HS.A-APR.1 (course model dependent); DoDEA CCRSM; NAEP: Algebra—symbolic manipulation; NCTM P2A: Practices 6, 7. Use this prompt-provided wording as the supporting standard description for this workflow.).

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