Question

Which of the following simplifies to the same expression as 4x2−3x2+5x−24 ?(1 point) Responses (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 4x(x−6) 4 x left parenthesis x minus 6 right parenthesis 2(x−12)

Answer 1

To determine which expression simplifies to \( 4x^2 - 3x^2 + 5x - 24 \), we first simplify the original expression.

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

   So the expression simplifies to: \[ x^2 + 5x - 24 \]

Now we can 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 the linear term).

The factors of \(-24\) that add up to \(5\) are \(8\) and \(-3\). Therefore, we can factor the quadratic as: \[ (x + 8)(x - 3) \]

Now, we can compare this with the given options:

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

Thus, the expression that simplifies to the same form as \( 4x^2 - 3x^2 + 5x - 24 \) is: \[ \boxed{(x + 8)(x - 3)} \]