Question 665005
The terms "linear polynomial" and "degree 1" are redundant.  A linear polynomial is a polynomial with degree 1.  The degree of the polynomial is equal to the highest degree of any term in the polynomial.  With those definitions, if the highest degree of any term in the polynomial is 1, then the polynomial is itself of degree 1, and therefore linear.
  
Roots are NOT negative integral exponents--they are fractional exponents.  In the case of a square root, the fractional exponent is {{{1/2}}}, so the degree of that term of the polynomial is also {{{1/2}}}.  As long as there is a term in the polynomial that is degree 1 (or higher), then having another term of degree {{{1/2}}} will not change the degree of the polynomial, since {{{1/2 < 1}}}