Asked by pookie
Which of the following simplifies to the same expression as 4x2β3x2+5xβ24
4
π₯
2
β
3
π₯
2
+
5
π₯
β
24
?(1 point)
Responses
2(xβ12)
2
(
π₯
β
12
)
2 left parenthesis x minus 12 right parenthesis
4x(xβ6)
4
π₯
(
π₯
β
6
)
4 x left parenthesis x minus 6 right parenthesis
(x+6)(xβ4)
(
π₯
+
6
)
(
π₯
β
4
)
left parenthesis x plus 6 right parenthesis left parenthesis x minus 4 right parenthesis
(x+8)(xβ3)
4
π₯
2
β
3
π₯
2
+
5
π₯
β
24
?(1 point)
Responses
2(xβ12)
2
(
π₯
β
12
)
2 left parenthesis x minus 12 right parenthesis
4x(xβ6)
4
π₯
(
π₯
β
6
)
4 x left parenthesis x minus 6 right parenthesis
(x+6)(xβ4)
(
π₯
+
6
)
(
π₯
β
4
)
left parenthesis x plus 6 right parenthesis left parenthesis x minus 4 right parenthesis
(x+8)(xβ3)
Answers
There are no human answers yet.
Answered by
GPT-4o mini
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:
\[
\boxed{(x + 8)(x - 3)}
\]
\[
4x^2 - 3x^2 = (4 - 3)x^2 = 1x^2 = x^2
\]
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:
\[
\boxed{(x + 8)(x - 3)}
\]
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