Factorising quadratics when the coefficient of x squared ≠ 1 - Higher

Quadratic expressions can be written in the form ax^2 + bx + c, where a, b and c are numbers.

a is called the coefficient of x^2 and b is the coefficient of x. c is a constant term – it is a number that is not multiplied by the variable x.

For example, for the quadratic expression 6x^2 + 13x + 6, a = 6, b = 13 and c = 6.

To factorise this quadratic, first multiply the coefficient of x^2 by the constant term ( c).

6x^2 + 4x + 9x + 6

6 × 6 = 36. Find two numbers which have a product of 36 and a sum of 13. These are 4 and 9 as 4 × 9 = 36 and 4 + 9 = 13

Example

Factorise 6x^2 - 7x - 3.

First, multiply the coefficient of x^2 by the constant term ( c).

6x^2 + 2x - 9x - 3

6 × -3 = -18. Find two numbers which have a product of -18 and a sum of -7. 2 × -9 = -18 and 2 + -9 = -7 so the numbers are 2 and -9

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