Question

Question Which of the following polynomial identities would result from dividing x2−a2 by x−a ? Enter the option number of the correct answer. Option #1: x2−a2=(x−a)(x+a) Option #2: x2−a2=(x−a)(x−a) Option #3: x2−a2=(x+a)(x+a) (1 point)

Answer 1

To determine which polynomial identity results from dividing \(x^2 - a^2\) by \(x - a\), we can use polynomial long division or factorization.

The expression \(x^2 - a^2\) can be factored as follows:

\[
x^2 - a^2 = (x - a)(x + a)
\]

This shows that \(x^2 - a^2\) indeed equals \((x - a)(x + a)\).

Now, let's check the options:

- **Option #1:** \(x^2 - a^2 = (x - a)(x + a)\) - This is correct.
- **Option #2:** \(x^2 - a^2 = (x - a)(x - a)\) - This is incorrect.
- **Option #3:** \(x^2 - a^2 = (x + a)(x + a)\) - This is incorrect.

Thus, the correct answer is **Option #1**.