Factorise and solve x^2-8x+15=0
Factorise means we want to turn x2-8x+15=0 into the form (x+a)(x+b)=0. We need to find the two whole numbers 'a' and 'b' which equal -8 (from the -8x part) when added together, i.e. a+b=-8, and equal 15 (from the +15 part) when multiplied together, i.e. ab=15. All whole numbers that multiply together to make 15 are: 1 and 15, -1 and -15 (since two negatives multiplied together make a positive), 3 and 5, -3 and -5 (again since two negatives multiplied together make a positive). Okay, so out of these four pairs, which pair adds together to make -8? It is -3 and -5. So that means a=-3 and b=-5. Now if we put that into the form we want, which is (x+a)(x+b)=0, we get: (x-3)(x-5)=0.
This is the factorised form of the equation. Now we want to solve it to find the values for x. We just have to make each bracket equal to zero. So set x-3=0. Adding 3 to both sides makes x-3+3=0+3. -3+3=0 and 0+3=3 of course, so we get x=3. Now do the same for the other bracket. Set x-5=0. Adding 5 to both sides in the same way as before makes x=5. So our answer is x=3 and x=5.
