Factorise x^2 - 6x + 9 = 0

x² - 6x + 9The method for factorising quadratics is to find 2 numbers that add to make the 'x' term (-6x in this case), and multiply together to make the final term (+9 in this case). Factors of +9 are: 1x9, -1x-9, 3x3, -3x-3. Therefore, in this case, the only factors that will also add to make -6 are -3 and -3. So, to factorise this, we simply put each into brackets with (x ± ?), so for this example they would both be (x-3). This means it would be acceptable to give the answer as (x-3)(x-3)=0 or (x-3)²=0, either are acceptable and that's as far as we need to go here as only factorisation was asked for, not solving.