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

Question

4
𝑥
2
−
3
𝑥
2
+
5
𝑥
−
24
?(1 point)
Responses

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

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

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

(x+6)(x−4)

Answer 1

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

\[ 4x^2 - 3x^2 + 5x - 24 = (4 - 3)x^2 + 5x - 24 = 1x^2 + 5x - 24 = x^2 + 5x - 24. \]

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

To 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 \(-3\) satisfy these conditions because:

• \(8 \cdot (-3) = -24\)
• \(8 + (-3) = 5\)

Thus, we can factor the expression as:

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

Now, let's review the given options:

1. \( (x + 8)(x - 3) \) - This matches our factorization.
2. \( 4x(x - 6) \) - This does not match.
3. \( 2(x - 12) \) - This does not match.
4. \( (x + 6)(x - 4) \) - This does not match.

The expression that simplifies to the same expression as \( 4x^2 - 3x^2 + 5x - 24 \) is:

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