2x^2+10x+7=0 factor this problem out
usually factors only contain rational numbers.
The roots of your equation are irrational, so there are no rational factors.
or
multiply the first times the last, 2 x 7 = 14
Are there any factors of 14 that add up to 10 ?
NO,
so there are no rational factors
or
evaluate the b^2-4ac of the quadratic equation formula
you would get 44
The √44 is irrational, so there are no rational factors.