which of the following polynomial identities would result from dividing x^3+a^3 by x+a enter the option number of the correct answer

Question

option 1: x^2+a^2
option 2: x^2-ax+a^2
option 3: x^2+ ax+a^2

Answer 1

To find which polynomial identity results from dividing \( x^3 + a^3 \) by \( x + a \), we can use the factorization of the sum of cubes. The sum of cubes can be factored as follows:

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

From this factorization, it is clear that when we divide \( x^3 + a^3 \) by \( x + a \), the quotient will be \( x^2 - ax + a^2 \).

Therefore, the correct option is:

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