Option B: [tex]y^{3}+y^{2}+7 y-10[/tex]
Option D: [tex]\frac{3}{4} x^{2}+5 y^{5}[/tex]
Solution:
Polynomial definition:
A polynomial can have constants, variables and exponents and fractional coefficient.
A polynomial cannot have fractional exponent, negative exponent and never division by a variable.
To select the expressions that would be considered as a polynomial.
Option A: [tex]6 x+y+\sqrt{x}+3[/tex]
√x is not, because the exponent is ½. Fractional exponents are not polynomials.
This is not a polynomial.
Option B: [tex]y^{3}+y^{2}+7 y-10[/tex]
A polynomial can have constants, variables and exponents.
This is a polynomial.
Option C: [tex]6 a^{\frac{1}{2}}+19[/tex]
Fractional exponents are not polynomials.
This is not a polynomial.
Option D: [tex]\frac{3}{4} x^{2}+5 y^{5}[/tex]
Fractional coefficients are allowed.
This is a polynomial.
Hence [tex]y^{3}+y^{2}+7 y-10[/tex] and [tex]\frac{3}{4} x^{2}+5 y^{5}[/tex] are polynomial.
