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The simplified term:
-4 \sqrt{2x+6} = - \sqrt{16(2x+6)}

Therefore this term has a fractional exponent,
 \sqrt{2x+x} = (2x)^{ \frac{1}{2} } + x^{ \frac{1}{2} }

BY DEFINITION OF POLYNOMIAL BY MATHEMATICIANS, it has to meet the following conditions:

1)  no fractional / negative exponent
2) no variable as denominator in any term.

The given has a fractional exponent.  When in simplified form, a variable is left under the radical symbol, the expression is not a polynomial.

So, the given expression IS NOT A POLYNOMIAL.

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