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

Question

Quizplus · Accepted Answer

We can group the first two terms and the last two terms:
$$x^3-2x^2+4x-8 = x^2(x-2)+4(x-2) = (x^2+4)(x-2)$$
Therefore, the correct factorization is $(x-2)(x^2+4)$. The only option that matches this factorization is (B).

Factor by Grouping x3−2x2+4x−8x ^ { 3 } - 2 x ^ { 2 } + 4 x - 8x3−2x2+4x−8

Factor by Grouping $x ^ { 3 } - 2 x ^ { 2 } + 4 x - 8$