Question

Select all of the expressions that would be considered a polynomial
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Answer 1

Option B:
`y^(3)+y^(2)+7 y-10`

Option D:
`(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+√(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^{(1)/(2)}+19`

Fractional exponents are not polynomials.

This is not a polynomial.

Option D:
`(3)/(4) x^(2)+5 y^(5)`

Fractional coefficients are allowed.

This is a polynomial.

Hence
`y^(3)+y^(2)+7 y-10` and
`(3)/(4) x^(2)+5 y^(5)` are polynomial.