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
Sure, I can help you with that!
To determine whether an expression is a polynomial, we need to check if it meets the criteria of a polynomial. A polynomial is an expression consisting of variables, coefficients, and only the operations of addition, subtraction, and multiplication. It does not include division by variables, negative exponents, or square roots.
In the given expression, 5x^3 + 2xy^4 + 6xy:
1. We have variables (x and y) and coefficients (5, 2, and 6).
2. We only have the operations of addition and multiplication, which are allowed in a polynomial.
3. We don't have any division by variables, negative exponents, or square roots.
Therefore, the given expression 5x^3 + 2xy^4 + 6xy is a polynomial because it meets all the criteria.
Now, let's determine the degree of the polynomial. The degree of a polynomial is the highest exponent of any variable in the expression.
In this case, the highest exponent is 4, which corresponds to y in the term 2xy^4. Therefore, the degree of the polynomial is 4.
So, the expression 5x^3 + 2xy^4 + 6xy is a polynomial of degree 4.