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

Question

Responses

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

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

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

2(x−12)

Answer 1

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

1. Combine like terms: \[ 4x^2 - 3x^2 = (4-3)x^2 = 1x^2 = x^2 \] So, the expression simplifies to: \[ x^2 + 5x - 24 \]

Next, we will factor \( x^2 + 5x - 24 \).

To factor this quadratic expression, we look for two numbers that multiply to -24 (the constant term) and add to 5 (the coefficient of x). The two numbers that satisfy these conditions are 8 and -3.

Thus, we can write: \[ x^2 + 5x - 24 = (x + 8)(x - 3) \]

Now, we can compare it with the options given in the question:

1. \( (x+6)(x-4) \)
2. \( (x+8)(x-3) \)
3. \( 4x(x-6) \)
4. \( 2(x-12) \)

From our factorization, we see that the expression \( x^2 + 5x - 24 \) simplifies to \( (x+8)(x-3) \).

Therefore, the correct answer is: \[ \boxed{(x+8)(x-3)} \]