Divide the polynomial x3−a3 by x−a . Which polynomial identity does this establish?(1 point)

Question

Responses

x3−a3=(x−a)(x2−ax−a2)
x cubed minus a cubed equals left parenthesis x minus a right parenthesis left parenthesis x squared minus a x minus a squared right parenthesis

x3−a3=(x−a)(x2+ax+a2)
x cubed minus a cubed equals left parenthesis x minus a right parenthesis left parenthesis x squared plus a x plus a squared right parenthesis

x3−a3=(x−a)(x2+ax−a2)
x cubed minus a cubed equals left parenthesis x minus a right parenthesis left parenthesis x squared plus a x minus a squared right parenthesis

x3−a3=(x−a)(x2−ax+a2)

Answer 1

To divide the polynomial \( x^3 - a^3 \) by \( x - a \), we can use polynomial long division or recognize it as a difference of cubes. The general factorization of a difference of cubes \( x^3 - a^3 \) is given by:

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

Thus, when we divide \( x^3 - a^3 \) by \( x - a \), we get:

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

This matches with our options. The correct polynomial identity established is:

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

Therefore, the correct response is:

x³−a³=(x−a)(x²+ax+a²)