Determine whether each epression is a polynomial. If it is tell if its a monomial, binomial, or trinomial.
x^2 + 1/3x
Answer: yes; monomial
x^2
---- no
y
-a^2b^3c^3d^4
My answer for the last one is yes; trinomial
To determine whether an expression is a polynomial, you need to check if it consists of one or more terms, each containing variables raised to whole number exponents. If an expression follows this pattern, it is a polynomial. Furthermore, we can further classify polynomials based on the number of terms they contain.
Now let's analyze each expression:
Expression 1: x^2 + 1/3x
- This expression contains two terms: x^2 and 1/3x.
- Both terms have variables raised to whole number exponents (2 and 1), so it satisfies the requirement for a polynomial.
- Since it has two terms, it is considered a binomial.
Expression 2: x^2
- This expression contains only one term: x^2.
- Since it has only one term, it is considered a monomial.
- As mentioned before, it is still a polynomial because it meets the requirement of having variables raised to whole number exponents.
Expression 3: y
- This expression contains only one term: y.
- Like the previous expression, it is a monomial since it has only one term and meets the criteria for a polynomial.
Expression 4: -a^2b^3c^3d^4
- This expression contains only one term with several variables raised to whole number exponents.
- Similarly, it is a monomial since it has only one term and meets the requirements for a polynomial.
In conclusion:
- The expression x^2 + 1/3x is a binomial polynomial.
- The expressions x^2, y, and -a^2b^3c^3d^4 are monomial polynomials.