To determine another name for the polynomial [tex]\( g(x) = 5x^9 + 17x^5 \)[/tex] based on the number of terms it contains, we will follow these steps:
1. Identify and count the terms:
- A "term" is a part of the polynomial that is added or subtracted.
- In the polynomial [tex]\( g(x) = 5x^9 + 17x^5 \)[/tex], there are two terms:
- The first term is [tex]\( 5x^9 \)[/tex]
- The second term is [tex]\( 17x^5 \)[/tex]
- Therefore, the polynomial has 2 terms.
2. Classify the polynomial based on the number of terms:
- Polynomials are typically classified based on the number of terms they contain:
- A monomial has just 1 term.
- A binomial has 2 terms.
- A trinomial has 3 terms.
- If a polynomial has more than 3 terms, it is generally referred to simply as a polynomial and not given a special name based on the number of terms.
Since [tex]\( g(x) = 5x^9 + 17x^5 \)[/tex] contains 2 terms, it is classified as a binomial.
Hence, another name for the polynomial [tex]\( g(x) = 5x^9 + 17x^5 \)[/tex], based on the number of terms it contains, is binomial.
