Polynomials (AQA A-Level Mathematics): Flashcards

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Factorisation
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Definition of factorisation

Reverse of expanding brackets, expressing as product of factors

General form: common factor factorisation

ax+ay=a(x+y)ax + ay = a(x + y)

Difference of squares formula

a2b2=(a+b)(ab)a^2 - b^2 = (a + b)(a - b)

Perfect square trinomial formula

a2+2ab+b2=(a+b)2a^2 + 2ab + b^2 = (a + b)^2

Factorising x2+bx+cx^2 + bx + c: properties of two numbers needed

Multiply to cc, add to bb

When to use factorising by grouping

When expression has four terms

Factorise 6x2+9x6x^2 + 9x

3x(2x+3)3x(2x + 3)

Factorise x29x^2 - 9

(x+3)(x3)(x + 3)(x - 3)

Factorise x2+6x+9x^2 + 6x + 9

(x+3)2(x + 3)^2

Factorising ax2+bx+cax^2 + bx + c (aeq1a eq 1): first step

Multiply aimesca imes c

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