Which of the following polynomial identities would result from dividing x2−a2

Question

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 the fact that \( x^2 - a^2 \) can be factored using the difference of squares formula:

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

When you divide \( x^2 - a^2 \) by \( x - a \), you effectively have:

\[ \frac{x^2 - a^2}{x - a} = x + a \]

This shows that \( x^2 - a^2 \) can be expressed as \( (x - a)(x + a) \).

Hence, the correct option is:

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