Use the Distributive Property to find which expression is equivalent to x^2−2x−8

Question

.(1 point)
Responses

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

(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 plus 4 right parenthesis

(x+4)(x−2)

Answer 1

To use the Distributive Property to factor the expression \( x^2 - 2x - 8 \), we need to find two numbers that multiply to \(-8\) (the constant term) and add up to \(-2\) (the coefficient of the \(x\) term).

The two numbers that satisfy these conditions are \( -4 \) and \( 2 \).

So, we can factor the expression as follows:

\[ x^2 - 2x - 8 = (x + 2)(x - 4) \]

Thus, the equivalent expression is:

\[ \boxed{(x+2)(x−4)} \]