Factor: $- 4 c ^ { 2 } + 8 c + 60$
A) $( c - 3 ) ( - 4 c + 20 )$
B) $- 4 ( c + 3 ) ( c - 5 )$
C) $- 4 ( c + 3 ) ( c + 5 )$
D) $( - 4 c + 5 ) ( c + 12 )$
E) Nonfactorable over the integers

Question

Quizplus · Accepted Answer

We can start by factoring out the greatest common factor of -4:
$$-4c^2 + 8c + 60 = -4(c^2 - 2c - 15)$$
Then we can factor the quadratic expression inside the parentheses by finding two numbers that multiply to -15 and add to -2:
$$c^2 - 2c - 15 = (c + 3)(c - 5)$$
Substituting this back into the original expression, we get:
$$-4(c^2 - 2c - 15) = -4(c + 3)(c - 5)$$
Therefore, the correct choice is B: $$-4(c + 3)(c - 5)$$

Factor −4c2+8c+60- 4 c ^ { 2 } + 8 c + 60−4c2+8c+60

Factor $- 4 c ^ { 2 } + 8 c + 60$