Factor the expression by grouping terms. $3 x ^ { 3 } + x ^ { 2 } - 15 x - 5$
A) $\left( x ^ { 2 } - 5 \right) ( 2 x + 1 )$
B) $\left( x ^ { 2 } - 6 \right) ( 3 x + 1 )$
C) $\left( x ^ { 2 } - 6 \right) ( 2 x + 1 )$
D) $\left( x ^ { 2 } + 5 \right) ( 3 x - 1 )$
E) $\left( x ^ { 2 } - 5 \right) ( 3 x + 1 )$

Question

Quizplus · Accepted Answer

We can use grouping method to factor the given expression:
$$3x^3 + x^2 - 15x - 5 = (3x^3 - 15x) + (x^2 - 5)$$
Now let's factor out the GCF from each group:
$$3x(x^2 - 5) + (x^2 - 5)$$
Notice that we have a common factor of $(x^2 - 5)$ that we can factor out:
$$(x^2 - 5)(3x+1)$$
Therefore, the answer is choice E.

Factor the Expression by Grouping Terms 3x3+x2−15x−53 x ^ { 3 } + x ^ { 2 } - 15 x - 53x3+x2−15x−5

Factor the Expression by Grouping Terms $3 x ^ { 3 } + x ^ { 2 } - 15 x - 5$