(x+7)(5x +2)
1) Let's factor the following expression 5x² +37x +14.
Checking the coefficients a =5, b= 37 and c= 14
Since a is different than 1 then we need another procedure.
2) We need to multiply a by c = 5 x 14 = 70 and look at b= 37.
Which are two numbers whose sum is 37 and their product is 70?
35 +2, and 35 x 2
Let's rewrite the whole expression, replacing it
5x² + 35x +2x +14 Instead of 37x write 35x +2x
5x² + 35x +2x +14 Group these terms
5x(x+7) +2(x+7) As we can see there's repetition so
(5x +2)(x+7)
3) Hence, the answer is 5x² +37x +14 = (5x +2)(x+7) or (x+7)(5x+2)