factorise x^2+10x+21

firstly the largest power is x^2 so when factorising we know that both brackets must involve an x plus or minus a number.

next we look at the 21 and we need two numbers that multiply together to get this number, the two sets of numbers that multiply to get this is 1 and 21 and 3 and 7.

then we take these two sets of numbers and we look at the 10x this means the numbers must add/subtract to give ten, this means the answer must use the 3 and 7 as they add to give 10

therefore our answer is (x+3)(x+7)