Question

Use the Distributive Property to find which expression is equivalent to x2−2x−8
.(1 point)
Responses

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

(x+2)(x−4)
left parenthesis x plus 2 right parenthesis left parenthesis x minus 4 right parenthesis

(x+4)(x−2)
left parenthesis x plus 4 right parenthesis left parenthesis x minus 2 right parenthesis

(x+2)(x+4)

Answer 1

To find which expression is equivalent to \( x^2 - 2x - 8 \) using the Distributive Property, we will look for factors of this quadratic expression.

1. We need to factor the expression. We are looking for two numbers that multiply to \(-8\) (the constant term) and add up to \(-2\) (the coefficient of the linear term).

2. The pairs of factors of \(-8\) are:
- \(1\) and \(-8\) (sum is \(-7\))
- \(2\) and \(-4\) (sum is \(-2\))
- \(-1\) and \(8\) (sum is \(7\))
- \(-2\) and \(4\) (sum is \(2\))

From the pairs, we can see that \(2\) and \(-4\) multiply to \(-8\) and add up to \(-2\).

3. Thus, we can factor \( x^2 - 2x - 8 \) as:
\[
(x + 2)(x - 4)
\]

Now we can find the correct response from the listed options:

- **(x + 4)(x - 4)** does not match.
- **(x + 2)(x - 4)** is the correct match.
- **(x + 4)(x - 2)** does not match.
- **(x + 2)(x + 4)** does not match.

The equivalent expression is **(x + 2)(x - 4)**.