is x^5+x^2+x a polynomial ? explain why or why not
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.
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.
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.
what is the degree of the x^5+x^2+x?
and can anybody explain how to get the degree thank you
To determine whether the expression x^5+x^2+x is a polynomial, we need to understand what a polynomial is.
A polynomial is an algebraic expression that consists of terms with positive integer exponents. The exponents must be whole numbers and cannot be negative or fractions.
In the given expression x^5+x^2+x, we can see that all the exponents are either 5, 2, or 1, which are positive integers. Therefore, x^5+x^2+x fulfills the requirement of having terms with positive integer exponents.
Hence, x^5+x^2+x is indeed a polynomial.