Question

which expression is equivalent to ( x^3 - x^2 - 14x + 24 )?
a ( (x - 2)(x - 3)(x + 4) )
b ( (x - 2)(x + 3)(x - 4) )
c ( (x + 2)(x - 3)(x - 4) )
d ( (x + 2)(x + 3)(x + 4) )

Explanation:

Step1: Expand Option A

First, multiply \((x - 2)(x - 3)\):

$$
LATEXBLOCK0
$$

Then multiply by \((x + 4)\):

$$
LATEXBLOCK1
$$

Step2: Verify Other Options (Optional)

For Option B: Expand \((x - 2)(x + 3)=x^2+3x - 2x - 6=x^2+x - 6\), then multiply by \((x - 4)\):

$$
LATEXBLOCK2
$$

For Option C: Expand \((x + 2)(x - 3)=x^2-3x + 2x - 6=x^2 - x - 6\), then multiply by \((x - 4)\):

$$
LATEXBLOCK3
$$

For Option D: Expand \((x + 2)(x + 3)=x^2+3x + 2x + 6=x^2+5x + 6\), then multiply by \((x + 4)\):

$$
LATEXBLOCK4
$$

Answer:

A. \((x - 2)(x - 3)(x + 4)\)