10. Factor the following: 8 x^2 - 2 x - 10 Factor 2 out of 8 x^2 - 2 x - 10: 2 (4 x^2 - x - 5)
Factor the quadratic 4 x^2 - x - 5. The coefficient of x^2 is 4 and the constant term is -5. The product of 4 and -5 is -20. The factors of -20 which sum to -1 are 4 and -5. So 4 x^2 - x - 5 = 4 x^2 - 5 x + 4 x - 5 = 4 x (x + 1) - 5 (x + 1): 2 4 x (x + 1) - 5 (x + 1) Factor x + 1 from 4 x (x + 1) - 5 (x + 1): Answer: 2 (x + 1) (4 x - 5) _____________________________________________
13. Factor the following: 16 x^2 - 24 x + 8
Factor 8 out of 16 x^2 - 24 x + 8: 8 (2 x^2 - 3 x + 1)
Factor the quadratic 2 x^2 - 3 x + 1. The coefficient of x^2 is 2 and the constant term is 1. The product of 2 and 1 is 2. The factors of 2 which sum to -3 are -1 and -2. So 2 x^2 - 3 x + 1 = 2 x^2 - 2 x - x + 1 = -(2 x - 1) + x (2 x - 1): 8 x (2 x - 1) - (2 x - 1)
Factor 2 x - 1 from x (2 x - 1) - (2 x - 1): Answer: 8 (2 x - 1) (x - 1)