Question

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

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

4x(x2+2x+3)
4 x left parenthesis x squared plus 2 x 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(4x+5x)

Answer 1

To determine which expression is equivalent to \( 4x^3 + 8x^2 + 12x \) using the Distributive Property, we can factor out the common term in the original expression.

The greatest common factor of the terms \( 4x^3 \), \( 8x^2 \), and \( 12x \) is \( 4x \).

Let's factor it out:

\[
4x^3 + 8x^2 + 12x = 4x(x^2 + 2x + 3)
\]

Now we can analyze the given options:

1. **(2x^2 + 4)(2x^2 + 3)** - This does not match because there is no \( 4x \) common factor.
2. **4x(x^2 + 2x + 3)** - This matches with our factored expression.
3. **(2x^2 + 4)(2x - 3)** - This does not match because it introduces different factors.
4. **4x(4x + 5x)** - This simplifies to \( 4x(9x) \), which does not match.

The correct response is:
**4x(x^2 + 2x + 3)**.