Question

8.
Factor the expression.

10g3 + 15g2 – 12g – 18


(5g2 – 6)(2g + 3)


(5g2 + 6)(2g – 3)


(5g2 + 3)(2g – 6)


(5g2 – 3)(2g + 6)

Answer 1

To factor the expression \(10g^3 + 15g^2 - 12g - 18\), we can use the grouping method.

First, let's group the terms in pairs that might reveal common factors:
\[ (10g^3 + 15g^2) + (-12g - 18) \]

Now factor out the greatest common factor (GCF) from each pair:
\[ 5g^2(2g + 3) - 6(2g + 3) \]

Notice that \((2g + 3)\) is a common factor in both groups:
\[ (5g^2 - 6)(2g + 3) \]

Therefore, the expression factors to:
\[ (5g^2 - 6)(2g + 3) \]

So, the correct answer is:
\[ (5g^2 - 6)(2g + 3) \]