Question

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

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

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

Now we can factor \( x^2 + 5x - 24 \). We need to find two numbers that multiply to \(-24\) (the constant term) and add to \(5\) (the coefficient of \(x\)). The numbers \(8\) and \(-3\) satisfy this:

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

Next, let's check the options provided:

1. \( (x + 6)(x - 4) \)
- This expands to: \( x^2 + 2x - 24 \) (not equal)

2. \( 2(x - 12) \)
- This expands to: \( 2x - 24 \) (not equal)

3. \( 4x(x - 6) \)
- This expands to: \( 4x^2 - 24x \) (not equal)

4. \( (x + 8)(x - 3) \)
- This, as shown earlier, simplifies to: \( x^2 + 5x - 24 \) (equals)

Therefore, the expression \( (x + 8)(x - 3) \) simplifies to the same expression as \( 4x^2 - 3x^2 + 5x - 24 \).