Solve the following equation by factorisation: x^2 - 2x -15 = 0

'No Nonsense' Answer: Our equation is x^2 - 2x - 15 = 0 so we want to find two numbers that add to get -2 and multiply to get - 15. The possible numbers pairs that multiply to get -15 are...1 and -15, -1 and 15, 3 and -5, -3 and 5. We can see that the only pair that add to get -2 is 3 and -5 (since 3 + -5 = -2) So we factorise it to look like this: (x+3)(x-5) = 0 To solve this we need either x+3=0 or x-5=0. Since (-3)+3=0 and (5)-5=0 we can have found our solutions... x=-3 or x=5. --------------------------------- Detailed Answer: To solve this we want to factorise "x^2 -2x - 15" into the form (x+a)(x+b). Now, if we expand (x+a)(x+b) we get x^2 + (a+b)x + ab. This means we have: (x+a)(x+b) = x^2 + (a+b)x + ab = x^2 -2x - 15 Comparing these two equations we can see that we have (a+b)x = -2x and ab = -15. If we work through the factors of -15 (which are 1,-1,3,-3,5,-5,15,-15) we can see that we should pick a and b equal to 3 and -5. So we have factorised the equation in the question to get: x^2 -2x - 15 = (x+3)(x-5) = 0 Since any number times zero is equal to zero, we can see either x+3=0 or x-5=0. If we solve these equations we then get the solutions: x=-3 or x=5