P2.2.1 - Simple algebraic division

Simple algebraic division; use of Only division by (ax + b) or (ax – b) will be required, e.g. the Factor Theorem and the b students should know that if f(x) = 0 when x =, Remainder Theorem. a then (ax – b) is a factor of f(x).; Students may be required to factorise cubic expressions such as x3 + 3x2 − 4 and 6x3 + 11x2 − x − 6.; Students should be familiar with the terms ‘quotient’ and ‘remainder’ and be able to determine the remainder when the polynomial f(x) is divided by (ax + b).

Use simple algebraic division to connect the rule to the data and decision in the question.

This matters because simple algebraic division determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply simple algebraic division to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Simple algebraic division is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.