Question

According to the Distributive Property, which expression is equivalent to 4x^3+8x^2+12x
?(1 point)
Responses

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

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

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

(2x^2+4)(2x^2+3)

Answer 1

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

First, let's factor out the greatest common factor (GCF) from \( 4x^3 + 8x^2 + 12x \):

1. The GCF of the coefficients \( 4, 8, \) and \( 12 \) is \( 4 \).
2. All terms contain \( x \), so we factor out \( 4x \).

Factoring \( 4x \) out of \( 4x^3 + 8x^2 + 12x \) gives us:

\[
4x(x^2 + 2x + 3)
\]

Now, we look at the response options provided:

1. \( (2x^2 + 4)(2x - 3) \)
2. \( 4x(4x + 5x) \)
3. \( 4x(x^2 + 2x + 3) \)
4. \( (2x^2 + 4)(2x^2 + 3) \)

The correct equivalent expression is:

**\( 4x(x^2 + 2x + 3) \)** (option 3).