Factor the polynomial
-$3 c^{2}+6 c d+3 d^{2}-75 f^{2}$
A) $3(c+d+5 f)(c+d-5 f)$
B) $(c+d+5 f)(c+d-5 f)$
C) $\left((c+d)^{2}+5 f\right)\left((c+d)^{2}-5 f\right)$
D) $3\left((c+d)^{2}+5 f\right)\left((c+d)^{2}-5 f\right)$

Question

Quizplus · Accepted Answer

The polynomial can be factored by first factoring out the greatest common factor, which is 3, resulting in $3(c^2 + 2cd + d^2 - 25f^2)$. Recognizing $c^2 + 2cd + d^2$ as a perfect square trinomial $(c+d)^2$ and $25f^2$ as a perfect square, the expression becomes $3((c+d)^2 - (5f)^2)$, which can be further factored into the difference of squares formula $a^2 - b^2 = (a+b)(a-b)$, resulting in $3(c+d+5f)(c+d-5f)$.

Factor the Polynomial - 3c2+6cd+3d2−75f23 c^{2}+6 c d+3 d^{2}-75 f^{2}3c2+6cd+3d2−75f2 A) 3(c+d+5f)(c+d−5f)3(c+d+5 f)(c+d-5 f)3(c+d+5f)(c+d−5f)

Factor the Polynomial
- $3 c^{2}+6 c d+3 d^{2}-75 f^{2}$ A) $3(c+d+5 f)(c+d-5 f)$