Question

According to the Distributive Property, which expression is equivalent to 4x3+8x2+12x
?(1 point)
Responses

4x(4x+5x)
4 x left parenthesis 4 x plus 5 x right parenthesis

(2x2+4)(2x2+3)
left parenthesis 2 x squared plus 4 right parenthesis left parenthesis 2 x squared plus 3 right parenthesis

(2x2+4)(2x−3)
left parenthesis 2 x squared plus 4 right parenthesis left parenthesis 2 x minus 3 right parenthesis

4x(x2+2x+3)
4 x left parenthesis x squared plus 2 x plus 3 right parenthesis

Answer 1

To determine which expression is equivalent to \(4x^3 + 8x^2 + 12x\), we can factor the original expression.

1. **Find the Greatest Common Factor (GCF):**
The GCF of the terms \(4x^3\), \(8x^2\), and \(12x\) is \(4x\).

2. **Factor out the GCF:**
\[
4x^3 + 8x^2 + 12x = 4x(x^2 + 2x + 3)
\]

Now we can see that \(4x(x^2 + 2x + 3)\) is present among the answer choices.

The only option that matches our factored expression is:
- **4x(x^2 + 2x + 3)**

So, the correct response is:
**4 x (x² + 2 x + 3)**.