Factorise fully x^2+6x+5=0

To start, notice that we have x^2 in our equation. This means that our answer is of the form (x )(x ). We now look for integers that give 5 when multiplied together. The only way we can do this is with the numbers 1 and 5. Our answer is now of the form (x 5)(x 1). To get the middle term, we add two of +5,+1,-1 or -5 such that the result is 6. We can see that only +5 and +1 sum to give 6. Our answer therefore is (x+5)(x+1)=0. Checking, we can see that our answer, when expanded, gives us x multiplied by x which equals x^2, 5 multiplied by 1 which is 5 and 5x plus 1x which is 6x, so we know our answer is correct.