The binomial (x + 5) is a factor of x2 + 8x + 15. what is the other factor?

Okay, if  is a factor of  then we know that  for some other factor which we don't know but want to find out.

is the highest power on the left side of the equation so we know we want something in the missing bracket that when we times it by x we get x². We therefore know that we need an x in the missing bracket and so it looks like this . When we expand that out we get the x² term (by multiplying the two x's) but also we get a +5x (from multiplying the 5 and the x) but by comparing it to the left hand side again, we see we want it to be +8x, we are +3x short. How can we get +3x?

If we add 3 to the missing bracket we get  so we have the  from the first expansion and now we have  from the second expansion. We have obtained the extra 3x we need to get to +8x but it has also added on 15 (by multiplying 3 and 5). Luckily, this is also part of the left hand side and sothe two sides match and we have found the missing factor: