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The Remainder Theorem and Factor Theorem — solving cubic equations and factorising polynomials.
Watch the full lesson before attempting practice questions.
Master these ideas before attempting exam questions.
When p(x) is divided by (x − a), the remainder equals p(a). No long division needed.
If p(a) = 0, then (x − a) is a factor of p(x). Use this to find factors of cubics.
Once a factor is found using the Factor Theorem, divide to get the quadratic factor, then factorise further.
1. Find a factor using trial and error (test x = ±1, ±2, ...). 2. Divide. 3. Solve the quadratic.
Commit these to memory — they appear in almost every exam.
These are your learning targets for Polynomials.
Avoid these errors — they cost marks every year.
The factor theorem uses (x − a) and substitutes x = a, not x = −a.
After finding one root, divide and factorise the resulting quadratic fully.
Be careful with negatives during polynomial long division. Show all steps.
Request CAPS-aligned study materials for Polynomials.
Comprehensive CAPS-aligned notes covering all key concepts, theorems, and worked examples for Polynomials.
NSC-style exam questions with full memorandum. Ideal for timed practice and self-assessment before exams.
Graded practice questions organised by difficulty. Perfect for building confidence before Paper 1.
Straight answers to the questions Grade 12 learners search most when studying polynomials for CAPS exams.
A polynomial is an algebraic expression made up of variables and constants combined using addition, subtraction, and multiplication. In Grade 12 CAPS, you will work with functions like quadratic, cubic, and higher-degree polynomials.
Start by looking for common factors, then apply methods like grouping, difference of squares, or the factor theorem. Practising past exam questions is the best way to master this skill.
The factor theorem states that if p(a) = 0, then (x - a) is a factor of the polynomial. This is commonly used to break down higher-degree polynomials.
The remainder theorem says that when a polynomial is divided by (x - a), the remainder is equal to p(a). This helps you avoid long division.
Focus on understanding factorisation, practise identifying patterns quickly, and always check your answers by substituting values. CAPS exams often repeat similar question styles.
Book a focused session with Chris Khomo and work through this topic step by step — at your own pace, online, from anywhere in South Africa.