First, we can factor out #x#, because all of the terms of the polynomial include #x#:
#=x(x^2+7x+10)# Now, looking at #(x^2+7x+10)#:
Since the #x^2# term's coefficient is one, we know the factoring will look something like:
#(x+-a)(x+-b)#. Looking at the other terms of the polynomial, we see that factors of #10# will have to add up to #7# (both are positive so both signs will be positive. Factors of 10:
#(1,10)#
#(2,5)#
And after this, it's the same in the opposite order. We can see that #2+5=7#, so #2# and #5# must go in to the equation:
#(x+2)(x+5)#. Inputting this into the other we get:
#x(x+2)(x+5)#
