Factor by grouping 5x^2+2x+40x+16

Factor the following:

5 x^2 + 40 x + 2 x + 16

2 x + 40 x = 42 x:

5 x^2 + 42 x + 16

Factor the quadratic 5 x^2 + 42 x + 16. The coefficient of x^2 is 5 and the constant term is 16. The product of 5 and 16 is 80. The factors of 80 which sum to 42 are 2 and 40. So 5 x^2 + 42 x + 16 = 5 x^2 + 40 x + 2 x + 16 = 8 (5 x + 2) + x (5 x + 2):

8 (5 x + 2) + x (5 x + 2)

Factor 5 x + 2 from 8 (5 x + 2) + x (5 x + 2):

Answer: (5 x + 2) (x + 8)