Which of the following simplifies to the same expression as 4x2−3x2+5x−24

Question

?(1 point)
Responses

(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

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

(x+8)(x−3)

Answer 1

To simplify the expression \( 4x^2 - 3x^2 + 5x - 24 \), we first combine like terms:

\[ 4x^2 - 3x^2 = 1x^2 \]

So the expression simplifies to:

\[ x^2 + 5x - 24 \]

Now we need to factor \( x^2 + 5x - 24 \). We are looking for two numbers that multiply to \(-24\) and add to \(5\). The numbers \(8\) and \(-3\) fit these conditions:

\[ x^2 + 5x - 24 = (x + 8)(x - 3) \]

Now, let's compare this result to the options provided:

1. \( (x + 6)(x - 4) \) → Expands to \( x^2 + 2x - 24 \) (not the same).
2. \( 2(x - 12) \) → Expands to \( 2x - 24 \) (not the same).
3. \( 4x(x - 6) \) → Expands to \( 4x^2 - 24x \) (not the same).
4. \( (x + 8)(x - 3) \) → We found this matches our factorization.

Therefore, the expression \( 4x^2 - 3x^2 + 5x - 24 \) simplifies to the same expression as option 4:

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