Question

State whether the expression is a polynomial. If it is, state the degree.

a) 3x^2 - 7x + 2 = yes;3
b) 3x - 2/x = No
c) sqrt2x^2 - 3pi = yes;2
sqrt2x + 5x = yes;1

Am I correct?

Answer 1

The degree is the sum of the highest powers of the variables.
In (a), which indeed is a polynomial, the highest power is in the first term, 3x², equal to 2.
(b) 2/x is not a non-negative integer power of the variable, so it is not a polynomial.
(c) The degree is 2 if the square-root radical applies only to the coefficient, i.e. √(2)x².
(d) Again, if the square-root radical applies only to the coefficient 2, i.e. √(2)x+5x, then it is a polynomial.
If it is √(2x)+5x, then it is not a polynomial, because polynomials do not contain fractional power terms.