How do you factorise a quadratic equation into the form (x+A)(x+B), for example x²+x-6 =0?
Quadratic equations are always given in the form ax2 +bx +c. One way of solving (finding values of x) and therefore factorising is to use the quadratic formula which is :x = −b ± √(b2 − 4ac)/ 2a ,using the values of a, b and c from the quadratic equation given. In the example given a=1 b=1 and c=-6 so when put in the formula: x = −1 + √(12 − 4(1x-6)) /2(1) = 2 or x = −1 -√(12 − 4(1x-6()/ 2(1) = -3 So here we have solved the equation but not factorised it. We know that x = 2 and x=-3. We also know that the equation = 0. Therefore when the equation is factorised into brackets the values within the brackets must =0. So if x=2, for the bracket to = 0 the value of A must be -2, and if x=-3 the value of B must be +3. Therefore x²+x-6 = (x-2)(x+3)
