How to solve a quadratic by factorisation?
There are 4 different methods to solve quadratics: factorisation, quadratic formula, graphically and completing the square. Today we shall solve equations by factorisation.Using the equation x2+ 6x + 8,1) We first multiply the coefficient (number before) of x2 and the constant (number not attached to an x). This would be 8[This step is more relevant when we have a number greater than one being the coefficient of x2.2) We then have to find 2 factors of this number that add up to equal the coefficient of x, that being 6 in this case. The factors of 8 are 1, 2, 4 and 8. Only 2 and 4 add up to make 6 and so this would be the numbers we use to make up the bracket3) In this case, as there is no coefficient of x2, the 2 and 4 make up the interior numbers of the bracket: (x+4)(x+2)In terms of proving this; we can rearrange the expression to include the factors of 2x and 4x; they will replace the 6x in the expression: x2 + 2x + 4x + 8.4) Factorise the quadratic as two linear expressions: x2+2 and 4x +8. this will become x(x+2) and 4(x+2)5) We then treat the duplicate bracket as one of our final factorised brackets then combine the factor on the outside to make our other bracket. therefore the final answer is (x+2)(x+4)
