Factor by grouping.
-$x^{3}+4 x^{2}+2 x+8$
A) $(x-4)\left(x^{3}+2\right)$
B) $(x+2)\left(x^{2}+4\right)$
C) $(x+4 x)\left(x^{2}+2\right)$
D) $(x+4)\left(x^{2}+2\right)$

Question

Quizplus · Accepted Answer

The correct factorization by grouping involves first grouping the terms as $(x^3 + 4x^2) + (2x + 8)$, then factoring out the common factors in each group. For the first group, $x^2$ can be factored out, leaving $x^2(x + 4)$. For the second group, 2 can be factored out, leaving $2(x + 4)$. Combining these gives $(x^2 + 2)(x + 4)$, which matches choice D.

Factor by Grouping x3+4x2+2x+8x^{3}+4 x^{2}+2 x+8x3+4x2+2x+8 A) (x−4)(x3+2)(x-4)\left(x^{3}+2\right)(x−4)(x3+2) B) (x+2)(x2+4)(x+2)\left(x^{2}+4\right)(x+2)(x2+4) C) (x+4x)(x2+2)(x+4 x)\left(x^{2}+2\right)(x+4x)(x2+2) D) (x+4)(x2+2)(x+4)\left(x^{2}+2\right)(x+4)(x2+2)

Factor by Grouping $x^{3}+4 x^{2}+2 x+8$ A) $(x-4)\left(x^{3}+2\right)$ B) $(x+2)\left(x^{2}+4\right)$ C) $(x+4 x)\left(x^{2}+2\right)$ D) $(x+4)\left(x^{2}+2\right)$