Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$27 c ^ { 3 } + 64$
A) $( 27 c + 4 ) \left( c ^ { 2 } - 12 c + 16 \right)$
B) $( 3 c + 4 ) \left( 9 c ^ { 2 } + 16 \right)$
C) $( 3 c + 4 ) \left( 9 c ^ { 2 } - 12 c + 16 \right)$
D) $( 3 c - 4 ) \left( 9 c ^ { 2 } + 12 c + 16 \right)$

Question

Quizplus · Accepted Answer

The expression $27c^3 + 64$ is a sum of cubes, which can be factored using the formula $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$. Here, $a = 3c$ and $b = 4$, so the factored form is $(3c + 4)(9c^2 - 12c + 16)$.

Factor Completely 27c3+6427 c ^ { 3 } + 6427c3+64 A) (27c+4)(c2−12c+16)( 27 c + 4 ) \left( c ^ { 2 } - 12 c + 16 \right)(27c+4)(c2−12c+16)

Factor Completely $27 c ^ { 3 } + 64$ A) $( 27 c + 4 ) \left( c ^ { 2 } - 12 c + 16 \right)$