Factorization 8

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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)

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