To classify each polynomial based on the number of terms it contains, we need to count the distinct terms in each polynomial. Here are the detailed steps and classifications:
### Polynomial 1: [tex]\(-2x^2 - x + 35\)[/tex]
1. Identify the terms: [tex]\(-2x^2\)[/tex], [tex]\(-x\)[/tex], [tex]\(+35\)[/tex].
2. There are three terms in total.
Classification: Trinomial (3 terms)
### Polynomial 2: [tex]\(10xx^3\)[/tex]
1. Simplify the expression: [tex]\(10xx^3 = 10x^4\)[/tex].
2. This expression simplifies to a single term.
Classification: Monomial (1 term)
### Polynomial 3: [tex]\(-x^2y^2 + 2y\)[/tex]
1. Identify the terms: [tex]\(-x^2y^2\)[/tex], [tex]\(+2y\)[/tex].
2. There are two terms in total.
Classification: Binomial (2 terms)
### Polynomial 4: [tex]\(x^2y^2 + 2y\)[/tex]
1. Identify the terms: [tex]\(x^2y^2\)[/tex], [tex]\(+2y\)[/tex].
2. There are two terms in total.
Classification: Binomial (2 terms)
### Polynomial 5: [tex]\(8 \cdot 2^2 + 0.25\)[/tex]
1. Simplify the expression: [tex]\(8 \cdot 2^2 = 32\)[/tex], so the polynomial is [tex]\(32 + 0.25\)[/tex].
2. Identify the terms: [tex]\(32\)[/tex], [tex]\(+0.25\)[/tex].
3. There are two terms in total.
Classification: Binomial (2 terms)
### Polynomial 6: [tex]\(x^3y^4 + 2x^2y - 3x\)[/tex]
1. Identify the terms: [tex]\(x^3y^4\)[/tex], [tex]\(+2x^2y\)[/tex], [tex]\(-3x\)[/tex].
2. There are three terms in total.
Classification: Trinomial (3 terms)
### Summary of Classifications:
1. [tex]\(-2x^2 - x + 35\)[/tex]: Trinomial (3 terms)
2. [tex]\(10xx^3\)[/tex]: Monomial (1 term)
3. [tex]\(-x^2y^2 + 2y\)[/tex]: Binomial (2 terms)
4. [tex]\(x^2y^2 + 2y\)[/tex]: Binomial (2 terms)
5. [tex]\(8 \cdot 2^2 + 0.25\)[/tex]: Binomial (2 terms)
6. [tex]\(x^3y^4 + 2x^2y - 3x\)[/tex]: Trinomial (3 terms)
So, the final classifications are:
[tex]\(\ [3, 1, 2, 2, 2, 3] \ \)[/tex]
