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Quadratic Equations by Factorising Flashcards
GCSE Mathematics (Edexcel) 1MA1
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Quadratic equation
An equation in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.
Factorising a quadratic
The process of rewriting a quadratic equation as a product of two linear factors.
Key step in solving by factorising
Set the quadratic equation equal to 0 before factorising.
Common factor in quadratics
Always check for a common factor first before factorising.
Product and sum method
Find two numbers that multiply to give the constant term (c) and add to give the coefficient of x (b).
Example: x² + 5x + 6 = 0
Factorises to (x + 2)(x + 3) = 0.
Solving after factorising
Set each factor equal to 0 and solve for x.
Example: (x + 2)(x + 3) = 0
Solutions are x = -2 and x = -3.
Difference of two squares
A quadratic in the form a² - b² can be factorised as (a + b)(a - b).
Example: x² - 9 = 0
Factorises to (x + 3)(x - 3) = 0, solutions are x = -3 and x = 3.
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