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

Question

?(1 point)
Responses

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

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

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

2(x−12)

Answer 1

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

1. Combine \(4x^2\) and \(-3x^2\): \[ 4x^2 - 3x^2 = 1x^2 = x^2 \]

2. We then write the expression: \[ x^2 + 5x - 24 \]

Now we want to factor the quadratic expression \(x^2 + 5x - 24\).

To factor \(x^2 + 5x - 24\), we look for two numbers that multiply to \(-24\) (the constant term) and add up to \(5\) (the coefficient of \(x\)). The numbers \(8\) and \(-3\) meet these criteria because:

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

Thus, we can factor the expression as: \[ (x + 8)(x - 3) \]

We can check the other options provided to determine which one simplifies to the same expression as \(4x^2 - 3x^2 + 5x - 24\):

1. \(4x(x-6)\): This expands to \(4x^2 - 24x\), which is not equivalent to \(x^2 + 5x - 24\).

2. \((x+8)(x-3)\): We found that this is the factored form of the quadratic \(x^2 + 5x - 24\).

3. \((x+6)(x-4)\): This expands to \(x^2 - 4x + 6x - 24 = x^2 + 2x - 24\), which is not equivalent.

4. \(2(x-12)\): This expands to \(2x - 24\), which is not equivalent.

Thus, the correct answer is: \[ \text{(x+8)(x−3)} \]