Factorise and solve x^2 - 8x + 15 = 0

Step 1: Factorise. In the final factorised form, your answer would be written in the form (x+a)(x+b). When expanded, this becomes: x^2 + (a+b)x + ab. Therefore, to factorise x^2 - 8x + 15, you need a + b = -8 and ab = 15. You know that a and b are both negative, as their addition is negative, but multiplication is positive. Finally, factors of 15 are: 1, 3, 5, 15. The only combination of numbers that work in this situation are 3 and 5. Therefore you know that a = -5 and b = -3. Factorised form is given as: (x-5)(x-3) = 0. Step 2: Solve. For two numbers to be multiplied together to make 0, one number must be 0 itself. Hence, either (x-5) = 0 or (x-3) = 0. We need to work on both scenarios, but I'll start with x-5 = 0. If x - 5 = 0, then x = 5 (you simply add 5 to the both sides). If x - 3 = 0, then x = 3 (same logic). Therefore, you obtain your two solutions, x = 5 and x = 3. At the end of your answer, state your two results clearly so your examiner can give you all the marks.