Question
Use a distributive property to find which expression is equivalent to x squared - 2x - 8
Answers
GPT-4o mini
To find an expression equivalent to \( x^2 - 2x - 8 \) using the distributive property, we can factor the quadratic expression.
The expression can be factored into two binomials. We are looking for two numbers that multiply to \(-8\) (the constant term) and add to \(-2\) (the coefficient of the \(x\) term).
These two numbers are \(-4\) and \(2\) since:
\[
-4 \times 2 = -8
\]
\[
-4 + 2 = -2
\]
Therefore, we can factor the expression as:
\[
x^2 - 2x - 8 = (x - 4)(x + 2)
\]
So, the expression equivalent to \( x^2 - 2x - 8 \) using the distributive property (i.e., factored form) is:
\[
(x - 4)(x + 2)
\]
The expression can be factored into two binomials. We are looking for two numbers that multiply to \(-8\) (the constant term) and add to \(-2\) (the coefficient of the \(x\) term).
These two numbers are \(-4\) and \(2\) since:
\[
-4 \times 2 = -8
\]
\[
-4 + 2 = -2
\]
Therefore, we can factor the expression as:
\[
x^2 - 2x - 8 = (x - 4)(x + 2)
\]
So, the expression equivalent to \( x^2 - 2x - 8 \) using the distributive property (i.e., factored form) is:
\[
(x - 4)(x + 2)
\]