Question

Which of the following simplifies to the same expression as 4x^2 – 3x^2 + 5x – 24?

A. (x + 8)(x – 3)
B. 2(x – 12)
C. 4x(x – 6)
D. (x + 6)(x – 4)

Answer 1

Let's simplify the expression \( 4x^2 - 3x^2 + 5x - 24 \) first.

\[
4x^2 - 3x^2 = (4 - 3)x^2 = 1x^2 = x^2
\]
So the original expression simplifies to:
\[
x^2 + 5x - 24
\]

Next, let's check each option to see if any simplify to \( x^2 + 5x - 24 \).

**Option A: \( (x + 8)(x - 3) \)**
\[
(x + 8)(x - 3) = x^2 - 3x + 8x - 24 = x^2 + 5x - 24
\]

This matches!

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

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

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

After checking all options, the only option that simplifies to the same expression as \( 4x^2 - 3x^2 + 5x - 24 \) is:

**A. \( (x + 8)(x - 3) \)**.