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 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 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 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 this represents a specific factorization related to the difference of cubes.
The expression \(x^3 - a^3\) can be factored as follows:
\[ x^3 - a^3 = (x - a)(x^2 + ax + a^2) \]
Thus, the correct polynomial identity that is established by dividing \(x^3 - a^3\) by \(x - a\) is:
\[ x^3 - a^3 = (x - a)(x^2 + ax + a^2) \]
So, the correct response is:
\(x^3 - a^3 = (x - a)(x^2 + ax + a^2)\)
