Factorization 8

1. Factor by grouping.

-4x + x² + 16 – 4x

Solution: - 4x + x² + 16 – 4x

= x² – 4x – 4x + 16

= x(x - 4) – 4(x - 4)

= (x - 4)(x - 4)

2. Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime.

14x² – 49x – 28

Solution: 14x² – 49x – 28

= 7(2x² – 7x - 4)

= 7[(2x² – 8x + x - 4)]

= 7[2x(x - 4) + 1(x - 4)]

= 7[(2x + 1)(x - 4)]

= 7(2x + 1)(x - 4)

3. Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime.

12x² – 13xt – 4t²

Solution: 12x² – 13xt – 4t²

= 12x² -16xt – 3xt – 4t²

= 3x(4x + t) – 4t(4x +t)

= (4x + t) (3x – 4)

4. Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime.

3x² + 11x - 20

Solution: 3x² + 11x – 20

= 3x² + 15x – 4x – 20

= 3x ( x + 5) – (x + 5)

= (x + 5) (3x – 4)