Which of the following polynomial identities would result from dividing x3+a3

by x+a
? Enter the option number of the correct answer.

Option #1: x2+a2


Option #2: x2−ax+a2


Option #3: x2+ax+a2


(1 point)

1 answer

To determine which polynomial identity results from dividing \(x^3 + a^3\) by \(x + a\), we can use the formula for the sum of cubes, which states:

\[ x^3 + a^3 = (x + a)(x^2 - ax + a^2) \]

Here, \(x^3 + a^3\) is factored into \((x + a)\) times \((x^2 - ax + a^2)\).

When you divide \(x^3 + a^3\) by \(x + a\), the quotient is \(x^2 - ax + a^2\).

Therefore, the correct option is:

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