Question

which of the following simplifes to the same expression as 4x^2 - 3x^2 + 5x -24? A) 2 (x-12) B) (x+6)(x-4) C) 4x(x-6) D) (x+8) (x-3)

Answer 1

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

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

Thus, the expression simplifies to:

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

Now we will factor \( x^2 + 5x - 24 \) to find its equivalent expression:

We need to factor this quadratic expression. We are looking for two numbers that multiply to \(-24\) (the constant term) and add up to \(5\) (the coefficient of the linear term).

The two numbers that satisfy these conditions are \(8\) and \(-3\) because:

\[
8 \times (-3) = -24
\]
\[
8 + (-3) = 5
\]

Thus, we can factor the expression as follows:

\[
x^2 + 5x - 24 = (x + 8)(x - 3)
\]

Now let's check which of the options given is equivalent to this expression:

A) \(2(x-12)\) - This does not factor to \(x^2 + 5x - 24\).

B) \((x+6)(x-4)\) - This expands to \(x^2 + 2x - 24\), which is not correct.

C) \(4x(x-6)\) - This expands to \(4x^2 - 24x\), which is also not correct.

D) \((x+8)(x-3)\) - This matches our factorization.

Thus, the correct answer is **D) \((x+8)(x-3)\)**.