Factorising ax² + bx + c Flashcards

GCSE Mathematics (Edexcel) 1MA1

Factorising ax² + bx + c

The process of rewriting a quadratic expression as a product of two linear factors.

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Factorising ax² + bx + c

The process of rewriting a quadratic expression as a product of two linear factors.

Key step in factorising ax² + bx + c

Find two numbers that multiply to ac (the product of a and c) and add to b.

Example: Factorise x² + 5x + 6

Find two numbers that multiply to 6 and add to 5 (2 and 3). Factorised form: (x + 2)(x + 3).

Example: Factorise 2x² + 7x + 3

Find two numbers that multiply to 6 (2×3) and add to 7 (6 and 1). Rewrite as 2x² + 6x + x + 3, then factorise: (2x + 1)(x + 3).

What to do if a = 1 in ax² + bx + c

If a = 1, find two numbers that multiply to c and add to b, then write as (x + m)(x + n).

What to do if a ≠ 1 in ax² + bx + c

If a ≠ 1, find two numbers that multiply to ac and add to b. Split the middle term and factorise in pairs.

Factorising by grouping

Split the middle term into two terms, group the terms in pairs, and factorise each pair.

Example: Factorise 3x² + 8x + 4

Find two numbers that multiply to 12 (3×4) and add to 8 (6 and 2). Rewrite as 3x² + 6x + 2x + 4, then factorise: (3x + 2)(x + 2).

How to check your factorisation

Expand the factorised form to ensure it simplifies back to the original quadratic expression.

Special case: Perfect square quadratics

If the quadratic is a perfect square (e.g., x² + 6x + 9), it can be written as (x + 3)².

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