NO, IT'S NOT.
The simplified term:
[tex]-4 \sqrt{2x+6} = - \sqrt{16(2x+6)} [/tex]
Therefore this term has a fractional exponent,
[tex] \sqrt{2x+x} = (2x)^{ \frac{1}{2} } + x^{ \frac{1}{2} } [/tex]
BY DEFINITION OF POLYNOMIAL BY MATHEMATICIANS, it has to meet the following conditions:
IN SIMPLIFIED FORM:
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.