Determine if the expression $-y^4$ is a polynomial or not. If it is a polynomial, state the type and degree of the polynomial.
Answer (2)
The expression − y 4 is a polynomial because it consists of a variable raised to a non-negative integer power.
The degree of the polynomial is 4, as the highest power of the variable y is 4.
The polynomial has one term, making it a monomial.
Therefore, the expression is a quartic monomial, and the answer is that it is a polynomial. Yes, it is a polynomial. Degree: 4, Type: Monomial
Explanation
Problem Analysis We are given the expression − y 4 and asked to determine if it is a polynomial. If it is, we need to state its type and degree.
Checking if the expression is a polynomial A polynomial is an expression consisting of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. The given expression − y 4 fits this definition. It has one term, a variable y , a coefficient − 1 , and the variable is raised to the power of 4, which is a non-negative integer.
Determining the degree Since the expression is a polynomial, we can identify its degree. The degree of a polynomial is the highest power of the variable in the expression. In this case, the variable y is raised to the power of 4. Therefore, the degree of the polynomial is 4.
Determining the type of polynomial The type of the polynomial can be determined based on the number of terms and its degree. Since the polynomial has only one term, it is a monomial. Since the degree is 4, it is a quartic monomial.
Final Answer Therefore, the expression − y 4 is a polynomial. It is a monomial of degree 4.
Examples
Polynomials are used to model various real-world phenomena. For example, the height of a ball thrown in the air can be modeled by a quadratic polynomial. Similarly, the growth of a population can be modeled by an exponential function, which can be approximated by a polynomial. Understanding polynomials helps us analyze and predict these phenomena.
The expression − y 4 is a polynomial because it consists of a variable raised to a non-negative integer power. It is a monomial with a degree of 4. Thus, the answer is that it is a polynomial, specifically a quartic monomial.
;
