Sure, let's classify each expression and determine their degree.
### 1. [tex]\(6x - 8\)[/tex]
- Type: This expression has two terms. Therefore, it is a binomial.
- Degree: The highest power of [tex]\(x\)[/tex] is 1, so the degree is 1.
### 2. [tex]\(a + b - c\)[/tex]
- Type: This expression has three terms. Therefore, it is a trinomial.
- Degree: Each variable [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] is to the power of 1. Hence, the degree is 1.
### 3. [tex]\(4x^3 + 6x^2 - x - 8\)[/tex]
- Type: This expression has four terms. Therefore, it is a polynomial (specifically, a four-term polynomial).
- Degree: The highest power of [tex]\(x\)[/tex] is 3, so the degree is 3.
### 4. [tex]\(x^3 y^2 z^2 + x^2 y^2 z\)[/tex]
- Type: This expression has two terms. Therefore, it is a binomial.
- Degree: To find the degree of a multivariable polynomial, we sum the exponents of the variables for each term and take the highest value.
- For [tex]\(x^3 y^2 z^2\)[/tex]: [tex]\(3 + 2 + 2 = 7\)[/tex]
- For [tex]\(x^2 y^2 z\)[/tex]: [tex]\(2 + 2 + 1 = 5\)[/tex]
Therefore, the degree is the highest sum, which is 7.
### 5. [tex]\(a^3 b c^2\)[/tex]
- Type: This expression has one term. Therefore, it is a monomial.
- Degree: Summing the exponents of all variables:
- For [tex]\(a^3\)[/tex]: [tex]\(3\)[/tex]
- For [tex]\(b\)[/tex]: [tex]\(1\)[/tex]
- For [tex]\(c^2\)[/tex]: [tex]\(2\)[/tex]
Therefore, the sum is [tex]\(3 + 1 + 2 = 6\)[/tex], so the degree is 6.
To summarize:
1. [tex]\(6x - 8\)[/tex]
- Type: Binomial
- Degree: 1
2. [tex]\(a + b - c\)[/tex]
- Type: Trinomial
- Degree: 1
3. [tex]\(4x^3 + 6x^2 - x - 8\)[/tex]
- Type: Polynomial (four-term polynomial)
- Degree: 3
4. [tex]\(x^3 y^2 z^2 + x^2 y^2 z\)[/tex]
- Type: Binomial
- Degree: 7
5. [tex]\(a^3 b c^2\)[/tex]
- Type: Monomial
- Degree: 6
