Factorise the expression x^2+5x-24.
Using the general form of a quadratic equation ax2+bx+c, we known that ax2+bx+c=(x+d)(x+e).The constant term, c, must be equal to the product of our two constants in the factorisation, therefore c=d x e.Applying this to our example x2+5x-24, then d x e=-24.The x term, b, must be equal to the sum of the two constants in the factorisation, therefore b=d+e.Again, applying this to our example, 5=d+e.So, to find both constant values for our factorisation that add together to equal 5 and multiply together to equal -24, which are 8 and -3.Therefore, x2+5x-24 can be factorised to (x+8)(x-3).
Note: Make sure to always expand out your factorisation to check your answer by ensuring you are left with the original quadratic equation.
