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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

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

(2x2+4)(2x−3)

1 answer

To find an expression equivalent to \( 4x^3 + 8x^2 + 12x \) using the Distributive Property, we first need to factor out the greatest common factor from the polynomial.

  1. Identify the greatest common factor (GCF) of the terms in \( 4x^3 + 8x^2 + 12x \):

    • The GCF is \( 4x \).

  2. Factor out \( 4x \) from each term: \[ 4x^3 + 8x^2 + 12x = 4x(x^2 + 2x + 3) \]

Among the provided choices, the expression that matches this factorization is:

  • \( 4x(x^2 + 2x + 3) \)

Thus, the equivalent expression is: 4x(x^2 + 2x + 3).