Question

Use the grouping method to factor 4x^3 + 20x^2 - 3x - 15

Answer 1

To factor the polynomial \( 4x^3 + 20x^2 - 3x - 15 \) using the grouping method, we will group the terms in pairs and then factor each group.

1. **Group the terms:**
\[
(4x^3 + 20x^2) + (-3x - 15)
\]

2. **Factor out the common factors from each group:**
- From the first group \( 4x^3 + 20x^2 \), we can factor out \( 4x^2 \):
\[
4x^2(x + 5)
\]
- From the second group \( -3x - 15 \), we can factor out \( -3 \):
\[
-3(x + 5)
\]

3. **Rewrite the expression using the factors:**
\[
4x^2(x + 5) - 3(x + 5)
\]

4. **Now notice that both groups contain the common factor \( (x + 5) \):**
\[
(x + 5)(4x^2 - 3)
\]

5. **The final factored form is:**
\[
(x + 5)(4x^2 - 3)
\]

Thus, the polynomial \( 4x^3 + 20x^2 - 3x - 15 \) factors to \( (x + 5)(4x^2 - 3) \).