Question

Which of the following simplifies to the same expression as 4x2−3x2+5x−24 ?(1 point) Responses (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) 2 left parenthesis x minus 12 right parenthesis (x+6)(x−4)

Answer 1

To determine which expression simplifies to \( 4x^2 - 3x^2 + 5x - 24 \), let's first simplify the given expression:

1. Combine like terms for \( 4x^2 - 3x^2 \):
\[
4x^2 - 3x^2 = 1x^2 = x^2
\]
So now we have:
\[
x^2 + 5x - 24
\]

Next, let's factor \( x^2 + 5x - 24 \).

We are looking for two numbers that multiply to \(-24\) (the constant term) and add to \(5\) (the coefficient of \(x\)). The numbers \(8\) and \(-3\) meet these criteria, since \(8 \times -3 = -24\) and \(8 + (-3) = 5\).

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

Now, comparing with the given options:
- \( (x + 8)(x - 3) \)
- \( 4x(x - 6) \)
- \( 2(x - 12) \)
- \( (x + 6)(x - 4) \)

The first option, \( (x + 8)(x - 3) \), is the same as \( x^2 + 5x - 24 \).

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