Factor by grouping.
-$$x ^ { 3 } + 5 x ^ { 2 } + 8 x + 40$$
A) $( x + 5 ) \left( x ^ { 2 } + 8 \right)$
B) $( x + 5 ) \left( x ^ { 2 } - 8 \right)$
C) $( x + 5 x ) \left( x ^ { 2 } + 8 \right)$
D) $( x - 5 ) \left( x ^ { 3 } + 8 \right)$

Question

Quizplus · Accepted Answer

To factor by grouping, we need to group together the first two terms and the last two terms. Then, we can factor out the greatest common factor from each group.

Grouping the first two terms, we get $x^3+5x^2=x^2(x+5)$.

Grouping the last two terms, we get $8x+40=8(x+5)$.

So the original expression becomes $x^2(x+5)+8(x+5)$. Now we can see that there is a common factor of $(x+5)$, which we can factor out:

$x^2(x+5)+8(x+5)=(x+5)(x^2+8)$

Therefore, the answer is choice A).

Factor by Grouping x3+5x2+8x+40x ^ { 3 } + 5 x ^ { 2 } + 8 x + 40x3+5x2+8x+40

Factor by Grouping $x ^ { 3 } + 5 x ^ { 2 } + 8 x + 40$