Question

Use the grouping method to factor 5x^3+15x^2-2x-6

Answer 1

To factor the polynomial \(5x^3 + 15x^2 - 2x - 6\) using the grouping method, we follow these steps:

1. **Group the Terms**: We can group the first two terms together and the last two terms together:
\[
(5x^3 + 15x^2) + (-2x - 6)
\]

2. **Factor Out Common Factors**:
- From the first group \(5x^3 + 15x^2\), we can factor out \(5x^2\):
\[
5x^2(x + 3)
\]
- From the second group \(-2x - 6\), we can factor out \(-2\):
\[
-2(x + 3)
\]

3. **Combine the Factored Groups**: Now our expression looks like this:
\[
5x^2(x + 3) - 2(x + 3)
\]

4. **Factor Out the Common Binomial**: We notice that \(x + 3\) is a common factor:
\[
(x + 3)(5x^2 - 2)
\]

Thus, the factored form of \(5x^3 + 15x^2 - 2x - 6\) is:
\[
\boxed{(x + 3)(5x^2 - 2)}
\]