can some one please help figure this problem out
Determine whether each expression is a polynomial.If it is a polynomial, state the degree of the polynomial.
5x^3+2xy^4+6xy
can someone please help me
Certainly! I can help you figure out whether the given expression is a polynomial and determine its degree.
A polynomial is an algebraic expression consisting of one or more terms, where each term is a product of a constant and one or more variables raised to non-negative integer exponents. It can contain addition and subtraction operations.
Let's examine the given expression: 5x^3 + 2xy^4 + 6xy
This expression consists of three terms: 5x^3, 2xy^4, and 6xy. Each term contains the variables x and y raised to non-negative integer exponents, and they are combined using addition.
Therefore, the given expression is a polynomial because it satisfies the definition.
Now, let's determine the degree of the polynomial. The degree of a polynomial is the highest power of the variable in any of its terms.
In the given expression, the highest power of the variable x is 3 in the term 5x^3, and the highest power of the variable y is 4 in the term 2xy^4. Since 3 is the highest power in the variable x and 4 is the highest power in the variable y, the degree of the polynomial is 4.
To summarize, the given expression 5x^3 + 2xy^4 + 6xy is a polynomial of degree 4.