Question

Which of the following simplifies to the same expression as 4x2−3x2+5x−24
?(1 point)
Responses

4x(x−6)
4 x left parenthesis x minus 6 right parenthesis

(x+8)(x−3)
left parenthesis x plus 8 right parenthesis left parenthesis x minus 3 right parenthesis

(x+6)(x−4)
left parenthesis x plus 6 right parenthesis left parenthesis x minus 4 right parenthesis

2(x−12)
2 left parenthesis x minus 12 right parenthesis

Answer 1

To determine which expression simplifies to the same expression as \( 4x^2 - 3x^2 + 5x - 24 \), we first simplify the given expression.

1. Combine like terms in \( 4x^2 - 3x^2 + 5x - 24 \):

\[
(4x^2 - 3x^2) + 5x - 24 = x^2 + 5x - 24
\]

Now we have the expression \( x^2 + 5x - 24 \).

Next, we will check each of the responses to see if any of them simplify to \( x^2 + 5x - 24 \).

1. **\( 4x(x - 6) \)**:
\[
4x(x - 6) = 4x^2 - 24x
\]
(This does not match.)

2. **\( (x + 8)(x - 3) \)**:
\[
(x + 8)(x - 3) = x^2 - 3x + 8x - 24 = x^2 + 5x - 24
\]
(This matches!)

3. **\( (x + 6)(x - 4) \)**:
\[
(x + 6)(x - 4) = x^2 - 4x + 6x - 24 = x^2 + 2x - 24
\]
(This does not match.)

4. **\( 2(x - 12) \)**:
\[
2(x - 12) = 2x - 24
\]
(This does not match.)

The only expression that simplifies to \( x^2 + 5x - 24 \) is \( (x + 8)(x - 3) \).

Thus, the correct response is:

\[
\boxed{(x + 8)(x - 3)}
\]