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 The amount that a letter has been multiplied by. In the example of 3a, the coefficient of a is 3 because 3 x a = 3a. 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 (\(c\)).
Image caption, 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
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Example
Factorise \(6x^2 - 7x - 3\).
First, multiply the coefficient of \(x^2\) by the constant term (\(c\)).
Image caption, 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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