How do you factorise a quadratic equation?

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A quadratic expression is of the form ax​2+bx+c. It is often useful to know what values of x will make the expression equal to 0; these are known as the roots of the equation. An easy way of seeing what these roots are is by factorisation of the equation (note that quadratic equations cannot always be factorised).

Starting with the general equation ax​2+bx+c = 0 we must look for a pair of numbers whose sum is equal to b and whose product is equal to c. So in the example x​2+2x+1 = 0 that would be 1 and 1, as 1+1 = 2 = b and 1x1 = 1 = c.

Once you have determined what the pair of numbers are you can put them into brackets like so: x​2+2x+1 = (x+1)(x+1).

Now for a second example where one of the numbers is negative. If x2​+2x-8 = 0 then the pair of numbers which add to 2 and multiply to give -8 is 4 and -2. We can now rewrite this in brackets as x2​+2x-8 = (x+4)(x-2).

Timothy W. GCSE Maths tutor, A Level Maths tutor

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