Question

Which algebraic expressions are polynomials? Check all that apply.

2x^3 - 1/x
x^3y - 3x^2 + 6x
y^2 + 5y - √ 3
2-√ 4x
-x√ 6
-1/3^x3 - 1/2^x2+ 1/4

Answer 1

2,3,5,6 are the correct answers

Answer 2

1.
`2x^3 - (1)/(x) =2x^3 - x^(-1)` is not a polynomial, because the degree of second term is negative (-1);

2.
`x^3y - 3x^2 + 6x` is a polynomial of 4th degree (the highest degree of all terms is 3+1=4);

3.
`y^2 + 5y - √(3)` is a polynomial of 2th degree (the highest degree of all terms is 2);

4.
`2- √(4x) =2-1x^{ (1)/(2) }` is not a polynomial, because the degree of second term is a fraction
`(1)/(2)`;

5.
`-x √(6)` is a monomial with 1st degree;

6.
`-(1/3)^(x^3) - (1/2)^(x^2)+ 1/4` is not a polynomial, because here the variable x is placed in degree.