Factor by grouping.
-$$2 x ^ { 3 } - 6 x ^ { 2 } - 6 x + 18$$
A) Not possible
B) $( x - 3 ) \left( 2 x ^ { 2 } - 6 \right)$
C) $( x + 18 ) \left( x ^ { 2 } - 6 x - 6 \right)$
D) $( x + 3 ) \left( 2 x ^ { 2 } - 6 \right)$

Question

Quizplus · Accepted Answer

To factor by grouping, we first split the expression into two groups: $2x^3 - 6x^2$ and $-6x + 18$. Factoring out the greatest common factor from each group gives us $2x^2(x - 3)$ and $-6(x - 3)$. Combining these gives us $(x - 3)(2x^2 - 6)$, which matches choice B.

Factor by Grouping 2x3−6x2−6x+182 x ^ { 3 } - 6 x ^ { 2 } - 6 x + 182x3−6x2−6x+18

Factor by Grouping $2 x ^ { 3 } - 6 x ^ { 2 } - 6 x + 18$