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 minus 4 right parenthesis

(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)

Answer 1

To use the Distributive Property to find an equivalent expression for \( x^2 - 2x - 8 \), we need to factor the quadratic expression.

The expression \( x^2 - 2x - 8 \) can be factored by finding two numbers that multiply to \(-8\) (the constant term) and add to \(-2\) (the coefficient of \(x\)).

The numbers that work are \( -4 \) and \( 2 \), because:
- \( -4 \times 2 = -8 \)
- \( -4 + 2 = -2 \)

Using these numbers, we can factor the expression as:
\[
(x - 4)(x + 2)
\]

Now, let's analyze the choices provided:

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

The first option, \((x + 2)(x - 4)\), is equivalent to our factored form since multiplication is commutative.

Thus, the correct equivalent expression is:
\[
\boxed{(x + 2)(x - 4)}
\]