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

Question

Responses

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

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

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

(x+6)(x−4)

Answer 1

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

1. Combine the 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 can factor the expression \(x^2 + 5x - 24\):

To factor \(x^2 + 5x - 24\), we need two numbers that multiply to \(-24\) (constant term) and add to \(5\) (coefficient of \(x\)). These two numbers are \(8\) and \(-3\) because:

\[ 8 \times (-3) = -24 \] \[ 8 + (-3) = 5 \]

Thus, we can factor the expression as: \[ (x + 8)(x - 3) \]

Now, we compare this with the provided options:

1. \(4x(x - 6)\) - Does not match because the degrees don't correspond.
2. \(2(x - 12)\) - Does not match as it simplifies to a linear term.
3. \((x + 8)(x - 3)\) - This matches our factored form.
4. \((x + 6)(x - 4)\) - Does not match because the numbers do not fit our earlier factorization.

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