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According to the Distributive Property, which expression is equivalent to 4x3+8x2+12x

4
𝑥
3
+
8
𝑥
2
+
12
𝑥
?(1 point)
Responses

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

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

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

4x(x2+2x+

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

To find the expression equivalent to \( 4x^3 + 8x^2 + 12x \) using the Distributive Property, we can start by factoring out the greatest common factor (GCF) from the terms in the expression.

The GCF of \( 4x^3, 8x^2, \) and \( 12x \) is \( 4x \).

Now, we can factor \( 4x \) out of the expression:

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

Now, let's evaluate the answer options provided:

1. \( (2x^2 + 4)(2x^2 + 3) \)
2. \( 4x(4x + 5x) \)
3. \( (2x^2 + 4)(2x - 3) \)
4. \( 4x(x^2 + 2x + 3) \) — This is the correct option.

Given the expression \( 4x(x^2 + 2x + 3) \) matches our factored form directly, the correct answer is:

**4x(x² + 2x + 3)**