Question

Select all of the expressions that would be considered a polynomial ​

Answer 1

Option B: $y^{3}+y^{2}+7 y-10$

Option D: $\frac{3}{4} x^{2}+5 y^{5}$

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: $6 x+y+\sqrt{x}+3$

√x is not, because the exponent is ½. Fractional exponents are not polynomials.

This is not a polynomial.

Option B: $y^{3}+y^{2}+7 y-10$

A polynomial can have constants, variables and exponents.

This is a polynomial.

Option C: $6 a^{\frac{1}{2}}+19$

Fractional exponents are not polynomials.

This is not a polynomial.

Option D: $\frac{3}{4} x^{2}+5 y^{5}$

Fractional coefficients are allowed.

This is a polynomial.

Hence $y^{3}+y^{2}+7 y-10$ and $\frac{3}{4} x^{2}+5 y^{5}$ are polynomial.