To identify the type of the polynomial [tex]\( a^2 + b - c d^3 \)[/tex], we will follow these steps:
1. Understand the structure of the polynomial: The polynomial given is [tex]\( a^2 + b - c d^3 \)[/tex]. Polynomials are mathematical expressions involving a sum of powers in one or more variables multiplied by coefficients.
2. Identify and count the terms: Each part of the polynomial that is separated by a plus ([tex]\(+\)[/tex]) or minus ([tex]\(-\)[/tex]) sign is considered a term.
- Here, [tex]\( a^2 \)[/tex] is the first term.
- [tex]\( b \)[/tex] is the second term.
- [tex]\( -c d^3 \)[/tex] is the third term.
3. Count the total number of terms: We have the following terms:
- [tex]\( a^2 \)[/tex]
- [tex]\( b \)[/tex]
- [tex]\( -c d^3 \)[/tex]
Therefore, there are 3 terms in this polynomial.
4. Determine the type of polynomial:
- A polynomial with one term is called a monomial.
- A polynomial with two terms is called a binomial.
- A polynomial with three terms is called a trinomial.
- A polynomial with four terms is called a four-term polynomial.
- Similarly, a polynomial with five terms is called a five-term polynomial.
- For polynomials with more than five terms, the terms are usually counted and specified.
Since our polynomial [tex]\( a^2 + b - c d^3 \)[/tex] consists of three terms, it is a trinomial.
Therefore, the type of the polynomial [tex]\( a^2 + b - c d^3 \)[/tex] is trinomial.
