Divide the polynomial x3−a3 by x−a . Which polynomial identity does this establish?(1 point) 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 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) 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)
1 answer
To divide the polynomial \( x^3 - a^3 \) by \( x - a \), we can use polynomial long division or recognize that \( x^3 - a^3 \) is a difference of cubes, which can be factored using the formula:
\[ x^3 - a^3 = (x - a)(x^2 + ax + a^2) \]
Thus, the polynomial identity established by dividing \( x^3 - a^3 \) by \( x - a \) is:
\[ x^3 - a^3 = (x - a)(x^2 + ax + a^2) \]
The correct response from the options you provided is:
\( x^3 - a^3 = (x - a)(x^2 + ax + a^2) \).
