How do you factorise quadratic equations?
Any quadratic equation, that is, an equation of the form ax2+bx+c=0, can be factorised, which means it is broken down into its linear factors. This means it will be of the form (x+m)(x+n). (We'll only consider the case a=1 for now.)To find the right m and n for a specific quadratic, we first multiply out the general form of the factorised version (using FOIL), and, simplifying, we get the form x2+(m+n)x+mn. Comparing this to our original equation, we can then see that we need to pick our m and n so that they add to the coefficient b, and they multiply to the coefficient c.eg. x2+2x-15.We know mn=-15, so we can just try all the pairs of numbers that might work, these are:(-1)15,1(-15),3*(-5), and (-3)*5.Since we then need them to add to make two, we know we want -3 and 5.So the factorised form of x2+2x-15 is (x+5)(x-3).
