Option A: z + 1Option B: 6 + wOption D: [tex]2 x^{4}-y[/tex]Solution:Let us first define the polynomial.A polynomial can have constants, variables, exponents and fractional coefficients.A polynomial cannot have negative exponents, fractional exponents and never divided by a variable.To find which expressions are polynomial:Option A: z + 1By the definition, z + 1 is a polynomial.It is polynomial.Option B: 6 + wBy the definition, 6 + w is a polynomial.It is polynomial.Option C: [tex]y^{2}-\sqrt[3]{y}+4[/tex][tex]y^{2}-\sqrt[3]{y}+4=y^{2}-{y}^{1/3}+4[/tex]Here, y have fractional exponent.So, it is not a polynomial.Option D: [tex]2 x^{4}-y[/tex]By the definition, [tex]2 x^{4}-y[/tex] is a polynomial.It is polynomial.Hence z + 1, 6 +w and [tex]2 x^{4}-y[/tex] are polynomials.