Question

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

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

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

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

(x+2)(x−4)

Answer 1

To find the expression that is equivalent to \( x^2 - 2x - 8 \) using the Distributive Property, we'll first factor the expression.

1. We need two numbers that multiply to \(-8\) (the constant term) and add up to \(-2\) (the coefficient of \(x\)).

The numbers that satisfy these conditions are \(2\) and \(-4\), since:
- \(2 \times -4 = -8\)
- \(2 + (-4) = -2\)

2. Thus, we can factor the quadratic expression as follows:
\[
x^2 - 2x - 8 = (x + 2)(x - 4)
\]

Now let's look at the options given:
1. \((x+2)(x+4)\)
2. \((x+4)(x-2)\)
3. \((x+4)(x-4)\)
4. \((x+2)(x-4)\)

The correct factored expression is \((x + 2)(x - 4)\).

So the correct answer is:
\[
\boxed{(x+2)(x-4)}
\]