2: Factor the following:
5 x^2 + 31 x + 6
Factor the quadratic 5 x^2 + 31 x + 6. The coefficient of x^2 is 5 and the constant term is 6.
The product of 5 and 6 is 30. The factors of 30 which sum to 31 are 1 and 30. So 5 x^2 + 31 x + 6 = 5 x^2 + 30 x + x + 6 = 6 (5 x + 1) + x (5 x + 1):6 (5 x + 1) + x (5 x + 1)
Factor 5 x + 1 from 6 (5 x + 1) + x (5 x + 1):
Answer: (5 x + 1) (x + 6)
4. Factor the following:
6 x^2 + 37 x + 6
Factor the quadratic 6 x^2 + 37 x + 6. The coefficient of x^2 is 6 and the constant term is 6. The product of 6 and 6 is 36. The factors of 36 which sum to 37 are 1 and 36. So 6 x^2 + 37 x + 6 = 6 x^2 + 36 x + x + 6 = 6 (6 x + 1) + x (6 x + 1):6 (6 x + 1) + x (6 x + 1)
Factor 6 x + 1 from 6 (6 x + 1) + x (6 x + 1):
Answer: (6 x + 1) (x + 6)
6. 6x² + x + 2 Trinomial can not be factored
