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)

Answer 1

To find which polynomial identity results from dividing \( x^2 - a^2 \) by \( x - a \), let's first recall that \( x^2 - a^2 \) can be factored using the difference of squares formula:

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

Now, let's analyze the options:

- **Option #1:** \( x^2 - a^2 = (x - a)(x + a) \) - This is correct, as it matches the factored form we found.
- **Option #2:** \( x^2 - a^2 = (x - a)(x - a) \) - This is incorrect because it implies \( x^2 - a^2 = (x - a)^2 \), which is not true.
- **Option #3:** \( x^2 - a^2 = (x + a)(x + a) \) - This is incorrect; it implies \( x^2 - a^2 = (x + a)^2 \), which is also not true.

The correct answer is:

**Option #1: \( x^2 - a^2 = (x - a)(x + a) \)**.