# Factorization 8

### From Homeworkwiki

**1. Factor by grouping.**

**-4x + x ^{2} + 16 – 4x**

**Solution:** - 4x + x^{2} + 16 – 4x

= x^{2} – 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.**

**14x ^{2} – 49x – 28**

**Solution:** 14x^{2} – 49x – 28

= 7(2x^{2} – 7x - 4)

= 7[(2x^{2} – 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.**

**12x ^{2} – 13xt – 4t^{2}**

**Solution:** 12x^{2} – 13xt – 4t^{2}

= 12x^{2} -16xt – 3xt – 4t^{2}

= 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.**

**3x ^{2} + 11x - 20**

**Solution:** 3x^{2} + 11x – 20

= 3x^{2} + 15x – 4x – 20

= 3x ( x + 5) – (x + 5)

= (x + 5) (3x – 4)