Question

List the names of the polynomials so they describe each polynomial based on the number of terms.

5xy^6
3m+7m^2-8m^2
17x^10=8x^7
5+6x+2x^2-4x^5
Other form of polyanion
binomial
monomial
trinomial

Answer 1

Here’s the classification of each polynomial based on the number of terms:

1. **5xy^6**: This is a **monomial** (1 term).

2. **3m + 7m^2 - 8m^2**: This simplifies to **3m - m^2** (since 7m^2 - 8m^2 = -m^2). This is still a **binomial** (2 terms after simplification).

3. **17x^10 = 8x^7**: The equation is not in polynomial form because of the equal sign. However, if considering just the polynomials on each side (17x^10 and 8x^7), we treat them separately as **monomials** (each having 1 term).

4. **5 + 6x + 2x^2 - 4x^5**: This is a **trinomial** (3 terms: 5, 6x, and 2x^2 when combined, excluding the -4x^5 as a separate term).

5. Other forms of polynomials could include any polynomial that does not fit into the classifications above, such as ones with 4 or more terms (e.g., a **quadrinomial** for 4 terms).

Given the above explanations, the appropriate classifications are:

1. **5xy^6** - Monomial
2. **3m + 7m^2 - 8m^2** - Binomial (after simplification)
3. **17x^10** and **8x^7** - Monomials
4. **5 + 6x + 2x^2 - 4x^5** - Trinomial