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) Option #

Answer 1

To find the correct polynomial identity resulting from dividing \( x^3 + a^3 \) by \( x + a \), we can apply polynomial long division or use the factorization of the sum of cubes.

The expression \( x^3 + a^3 \) can be factored using the identity:

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

From this factorization, we can see that \( x + a \) is a factor, and when we divide \( x^3 + a^3 \) by \( x + a \), we are left with the quotient:

\[ x^2 - ax + a^2 \]

Thus, the answer corresponds to Option #2.

Therefore, the correct option is:

Option #2: x² - ax + a²