Question

is x^5+x^2+x a polynomial ? explain why or why not

Answer 1

Yes it is a polynomial, because each term qualifies as a monomial, composed of the product of one or more non-negative integer powers of variables multiplied by a coefficient which is a real number or a constant.

Example:
4x^2 + 2x + 3 is a polynomial
4√x + 2x is NOT a polynomial, because √x is not a non-negative integer power of x.

Answer 2

Sam,
This expression is a trinomial.
You have coefficients that represent 1 (x's) and you have your exponents of 5 and 2. That is all you need for a polynomial. The third x makes it a trinomial.

Answer 3

what is the degree of the x^5+x^2+x?
and can anybody explain how to get the degree thank you

Answer 4

The degree of a polynomial is the highest sum of the exponents of the individual variables of each term (monomial).

Here there is only one variable x, so the highest exponent is 5 (in x^5).
The degree is therefore 5.

If the polynomial had been 5, the degree would be 0, since 5 is the same as 5x^0.