Factorise fully X^2 - 6X + 8

Factorising means reducing an equation to a set of brackets, in the form (x+a)(x+b), where a and b are constants. To factorise this equation, we must find two numbers that add to make -6, and multiply to make 8. An easy way to approach this is to list the factors of 8 in pairs, and see which pair adds to make -6. The pairs are (8,1) and (2,4), but when we add these, we cannot make -6. Both answers are positive. At this point, we can recall that the multiplication of two negative numbers is equal to a positive answer, so we can test the negative pairs of factors that still multiply to 8. These are (-1, -8) and (-2, -4). Now, we can see that whilst -1 + -8 = -9, -2 + -4= -6. Therefore, the pair of number in the brackets is (-2,-4), since these add to make -6 and multiply to make 8. Filling in the blanks of the original equation, we are left with (x-2)(x-4).