Question

extra practice
in exercises 1–18, factor the polynomial.

1. ( 2c^2 - 14c - 36 )
2. ( 4a^2 + 8a - 140 )
3. ( 3x^2 - 6x - 24 )

Explanation:

Step1: Factor out GCF of first polynomial

$2c^2 - 14c - 36 = 2(c^2 - 7c - 18)$

Step2: Factor quadratic inside parentheses

$c^2 - 7c - 18 = (c - 9)(c + 2)$

Step3: Combine for first polynomial

$2(c - 9)(c + 2)$

Step4: Factor out GCF of second polynomial

$4a^2 + 8a - 140 = 4(a^2 + 2a - 35)$

Step5: Factor quadratic inside parentheses

$a^2 + 2a - 35 = (a + 7)(a - 5)$

Step6: Combine for second polynomial

$4(a + 7)(a - 5)$

Step7: Factor out GCF of third polynomial

$3x^2 - 6x - 24 = 3(x^2 - 2x - 8)$

Step8: Factor quadratic inside parentheses

$x^2 - 2x - 8 = (x - 4)(x + 2)$

Step9: Combine for third polynomial

$3(x - 4)(x + 2)$

Answer:

1. $2(c - 9)(c + 2)$
2. $4(a + 7)(a - 5)$
3. $3(x - 4)(x + 2)$