If a factored form of a polynomial $X^3$ is $X \times X \times X$, what would be the factored form of a square root, which I learned was $X^{1/2}$
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$\begingroup$ This has nothing to do with linear algebra $\endgroup$– ShaileshCommented Nov 16, 2015 at 23:29
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1$\begingroup$ Give me a definition of "factored form" and I can tell you the answer. So far, the answer doesn't really have an answer. $\endgroup$– 5xumCommented Nov 16, 2015 at 23:33
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2 Answers
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$X^{1/2}$ is not a polynomial, in the sense that there is no polynomial $p(X)$ such that $P(X)^2=X$. Indeed, the degree of $P(X)^2$ is even, whereas the degree of $X$ is odd.
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You can "factor" a monomial (like $X^3$) however you like, by your definition. Yes, $X^3 = X*X*X$ , but $X^3$ also equals $X^.5 * X^.5 * X^.5 * X^.5 * X^.5 * X^.5.$ By this logic, there is an infinite amount of ways to "factor" any monomial.
