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

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

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

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

(x+8)(x−3)

Answer 1

To simplify \( 4x^2 - 3x^2 + 5x - 24 \), we can first combine the like terms:

\[ 4x^2 - 3x^2 = (4 - 3)x^2 = 1x^2 = x^2 \]

So, we can rewrite the expression as:

\[ x^2 + 5x - 24 \]

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

We need to find two numbers that multiply to \(-24\) (the constant term) and add to \(5\) (the coefficient of the linear term). The numbers \(8\) and \(-3\) satisfy this:

\[ 8 + (-3) = 5 \quad \text{and} \quad 8 \times (-3) = -24 \]

So, we can factor the quadratic as:

\[ (x + 8)(x - 3) \]

Now, we can compare this factorization with the options given:

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

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

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