Three worksheets on dividing monomials by monomials and polynomials by monomials or polynomials. The following resources are included:

• Dividing Monomials
• Dividing a Polynomial By a Monomial
• Dividing polynomials
  Solutions to all worksheets are included.

Help your KS3, GCSE, and A-Level Mathematics students master polynomial division with this structured, 3-worksheet practice bundle. This comprehensive resource guides pupils through a complete, step-by-step skill progression: applying the quotient rule of index laws to monomials, dividing polynomials by single terms, and performing full polynomial long division.

Whether you need a ready-to-use main lesson task, homework packet, cover work, or revision assignment, this resource is designed to reduce teacher workload while building student fluency in algebra.

What’s Included in This Bundle:

• Worksheet 1: Dividing Monomials: Practice quotient rule of indices, multi-variable terms, and simplifying algebraic fractions.
• Worksheet 2: Dividing Polynomials by Monomials: Term-by-term fraction splitting, negative coefficients, and rational outcomes.
• Worksheet 3: Dividing Polynomials by Polynomials: Structured practice on polynomial long division with and without remainders.
• Full Step-by-Step Answer Keys: Complete worked solutions included for effortless marking or pupil self-assessment.

Skill Progression Covered:

• Index Laws & Monomials: Apply the quotient rule to simplify single and multi-variable terms.
• Algebraic Fractions & Negative Powers: Build fluency simplifying complex algebraic terms and rational expressions.
• Polynomial-by-Monomial Division: Split numerator terms over common monomial denominators.
• Polynomial Long Division: Divide linear, quadratic, cubic, and quartic polynomials with integer remainders.

Ideal For:

• Key Stage 3 (Years 8–9): Index laws and basic algebraic manipulation.
• Key Stage 4 / GCSE Math (Foundation & Higher Tier): Simplifying algebraic fractions and operations with indices.
• Key Stage 5 / A-Level Math: Polynomial long division and algebraic manipulation.
• Lesson Uses: Independent practice, homework, revision/retrieval practice, cover work, or small-group intervention.

UK Curriculum Alignment:

• KS3 Programme of Study: Algebra – Simplify and manipulate algebraic expressions (including those involving powers and indices).
• GCSE Maths (AQA, Edexcel, OCR): Topic A4 – Simplify and manipulate algebraic expressions by collecting like terms, multiplying a single term over a bracket, taking out common factors, and applying index laws.
• A-Level Maths (Pure Mathematics): Topic 1.3 – Simplify rational expressions including by factorising and algebraic division (by linear and quadratic denominators).