Question

Which of the following simplifies to the same expression as 4x2−3x2+5x−24 ?(1 point) Responses (x+6)(x−4) left parenthesis x plus 6 right parenthesis left parenthesis x minus 4 right parenthesis (x+8)(x−3) left parenthesis x plus 8 right parenthesis left parenthesis x minus 3 right parenthesis 2(x−12) 2 left parenthesis x minus 12 right parenthesis 4x(x−6)

Answer 1

Let's simplify the expression \(4x^2 - 3x^2 + 5x - 24\).

1. Combine the like terms: \[ 4x^2 - 3x^2 = x^2 \] So the expression becomes: \[ x^2 + 5x - 24 \]

2. Next, we need to factor this expression \(x^2 + 5x - 24\). We need two numbers that multiply to \(-24\) (the constant term) and add to \(5\) (the coefficient of the \(x\) term). The numbers \(8\) and \(-3\) satisfy these conditions: \[ 8 \times (-3) = -24 \quad \text{and} \quad 8 + (-3) = 5 \]

3. Therefore, we can factor the expression: \[ x^2 + 5x - 24 = (x + 8)(x - 3) \]

Now, we can match our result with the provided options. The expression that simplifies exactly to \(4x^2 - 3x^2 + 5x - 24\) is:

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

So, the correct answer is \((x + 8)(x - 3)\).