document.write( "Question 1086959: Determine whether the function is a polynomial function.\r
\n" ); document.write( "\n" ); document.write( "f(x) = x^3/2 - x^6 + 6
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\n" ); document.write( "\n" ); document.write( "No
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\n" ); document.write( "\n" ); document.write( "Yes \n" ); document.write( "

Algebra.Com's Answer #701215 by mathmate(429) $\"\"$ $\"About$

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Question:
\n" ); document.write( "Determine whether the function is a polynomial function.
\n" ); document.write( "f(x) = x^3/2 - x^6 + 6
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\n" ); document.write( "Solution:
\n" ); document.write( "This question shows the importance of the PEMDAS rules, and why we should stick to the rules.
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\n" ); document.write( "A polynomial is an expression of *one or more* algebraic terms, especially the sum of several terms that contain different *non-negative integrer* powers of the same variable(s).
\n" ); document.write( "(above definition is adapted from Google definition, which defines poly in the usual sense of two or more. In math, a monomial is also considered a polynomial for generality, also, the important condition of *non-negative integer* powers was added).\r
\n" ); document.write( "\n" ); document.write( "As it is, the rules of PEMDAS interpret the function as:
\n" ); document.write( "f(x) = (x³)/2 - x^6 +6 [exponential before multiplication/division]
\n" ); document.write( "which makes it a polynomial, because the powers are non-negative integer powers.
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\n" ); document.write( "However, I have a hunch that the question was meant to read
\n" ); document.write( "f(x) = x^3/2 - x^6 +6
\n" ); document.write( "which makes it a non-integer power, and therefore this second case is not a polynomial. The answer can only be determined after confirmation of the question. \n" ); document.write( "

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