8.

Factor the expression.

8g3 + 10g2 – 12g – 15

(2g2 – 5)(4g + 3)

(2g2 + 5)(4g – 3)

(2g2 – 3)(4g + 5)

(2g2 + 3)(4g – 5)

1 answer

Let's factor the expression \(8g^3 + 10g^2 - 12g - 15\).

First, we can try to group the terms in pairs:

\[
(8g^3 + 10g^2) + (-12g - 15)
\]

We can factor out the greatest common factor from each pair:

\[
2g^2(4g + 5) - 3(4g + 5)
\]

Next, we observe that each group contains a common factor, \(4g + 5\):

\[
(2g^2 - 3)(4g + 5)
\]

So the expression \(8g^3 + 10g^2 - 12g - 15\) factors to:

\[
(2g^2 - 3)(4g + 5)
\]

Therefore, the correct answer is:

\[
(2g^2 - 3)(4g + 5)
\]

So, the correct option is:

\[
(2g^2 - 3)(4g + 5)
\]