Factor by grouping.
-$$x ^ { 4 } - x ^ { 3 } + 4 x - 4$$
A) $\left( x ^ { 3 } + 4 \right) ( 4 x - 1 )$
B) $\left( x ^ { 3 } + 4 \right) ( x - 1 )$
C) $\left( x ^ { 3 } - 1 \right) ( x + 4 )$
D) $\left( x ^ { 3 } - 4 \right) ( x - 1 )$

Question

Quizplus · Accepted Answer

To factor by grouping, we first split the expression into two groups: $x^4 - x^3$ and $4x - 4$. Factoring out the greatest common factor from each group gives us $x^3(x - 1) + 4(x - 1)$. Notice that $x - 1$ is a common factor, so we can factor it out to get $(x^3 + 4)(x - 1)$, which matches choice B.

Factor by Grouping x4−x3+4x−4x ^ { 4 } - x ^ { 3 } + 4 x - 4x4−x3+4x−4

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