Real Polynomials.
Use polynomial structure, division and root theorems to solve equations and explain real polynomial graphs.
Work through the topic
Learn the method, follow the examples, then try the worksheet.
- 01
Polynomial notation and operations
Recognise polynomial expressions and calculate with them without losing terms or signs.
- 02
Zeros, roots and factors
Connect real roots with zeros and factors, including repeated roots.
- 03
Polynomial identities and coefficient comparison
Find unknown polynomial coefficients by comparing powers and distinguish identities from equations.
- 04
Polynomial division
Divide polynomials and express the result as dividend equals divisor times quotient plus remainder.
- 05
Remainder theorem
Find remainders by substitution and use given remainders to determine unknown coefficients.
- 06
Factor theorem
Use the factor theorem to prove a linear factor exists and determine missing coefficients.
- 07
Finding and factorising real polynomial roots
Find real roots systematically and factor as far as possible over the real numbers.
- 08
Graphing real polynomials
Use roots, multiplicity, intercepts and leading terms to explain the shape of a real polynomial graph.
- 09
Solving real polynomial equations
Solve real polynomial equations by structure and reject solutions that do not fit an application.
Topic review
Revisit the key ideas, then choose a practice paper.