Polynomial Long Division & Factoring Polynomials Worksheet + Answer Key

Factoring Polynomials with Long Division & Factor Theorem (with Solutions)

A collection of three worksheets on the following topics: * Dividing polynomials using long division * Using division to factor polynomials * Factorising a polynomial using the factor theorem In the first worksheet, students are required to perform long division for some given pairs of polynomials. In the second worksheet, students must use polynomial division to find the remaining linear factors of a polynomial, given one of its factors. In other exercises, students must find a polynomial using multiplication given all its factors, find the highest common factor of given algebraic expressions and find missing terms in factorized expressions. In the third worksheet, students are required to check whether a given polynomial is a factor of another polynomial by using the factor theorem and then in some other exercises they are required to factor cubic polynomials by first finding one of its linear factors (by checking given polynomials or inspecting using the factor theorem) and then using long division to find the remaining linear factors. Detailed solutions are included. Master polynomial long division and algebraic factoring with this comprehensive, no-prep worksheet pack! Includes 18 high-quality practice questions covering cubic and order 4 polynomial division, the Factor Theorem, finding missing terms, and fully factorising expressions into linear components. Comes complete with full, step-by-step worked solutions for every problem—ideal for A-Level Maths, GCSE Further Maths, homework, or independent study. ________________________________________ Looking for a rigorous, ready-to-print resource to help your students master algebraic division and advanced factorisation? This comprehensive worksheet pack breaks down complex algebraic concepts into clear, manageable practice tasks. Whether your students are learning polynomial long division for the first time or reviewing the Factor Theorem for their A-Level calculus preparation, this resource provides the structured layout they need to build true mathematical fluency. This resource requires zero preparation—simply download, print, and distribute directly to your classes. ________________________________________ **What’s Covered in This Pack?** • Polynomial Long Division: Practice dividing cubic and order 4 polynomials by linear and quadratic expressions (with and without remainders). • The Factor Theorem: Step-by-step algebraic substitution to prove whether a given linear expression is a factor of a polynomial. • Fully Factorising Expressions: Advanced problems requiring students to use a known linear factor to break down cubic and quartic expressions into a product of linear components. • Missing Terms & HCF Practice: Short puzzles designed to test structural understanding by finding missing coefficients and determining the Highest Common Factor (HCF). ________________________________________ **What is Included?** • Printable Student Worksheets: Clean, professionally formatted pages with clear directions and ample workspace for pupils. • Full Step-by-Step Solutions: Complete worked answers showing every single subtraction step, remainder, and factorisation stage. Perfect for self-marking or saving you valuable time! ________________________________________ **Perfect For:** • Key Stage 4 (GCSE): Further Maths or higher-tier extension work. • Key Stage 5 (A-Level): Pure Mathematics core revision (Year 12 / Year 13). • Cover Lessons: Structured and self-contained, making it excellent for supply teachers. • Homework & Independent Study: Ideal for reinforcing classroom learning.