To determine which expression is a linear binomial, let's first understand the terms we'll be working with:
1. Binomial: A polynomial with exactly two terms.
2. Linear Polynomial: A polynomial of degree 1, which means the highest power of the variable is 1.
Given this information, let's analyze each option:
1. Option 1: 4
- This expression consists of only one term and is simply a constant.
- It is not a binomial because it doesn't have two terms.
- It is not linear since linear polynomials must have a variable term with the highest power of 1.
2. Option 2: [tex]\(2x + 3x^3 - 1\)[/tex]
- This expression has three terms: [tex]\(2x\)[/tex], [tex]\(3x^3\)[/tex], and [tex]\(-1\)[/tex].
- It is not a binomial because it has more than two terms.
- Moreover, the term [tex]\(3x^3\)[/tex] is of degree 3, which makes it a non-linear polynomial.
3. Option 3: [tex]\(3x^2 - 2\)[/tex]
- This expression has two terms: [tex]\(3x^2\)[/tex] and [tex]\(-2\)[/tex].
- It is a binomial because it has exactly two terms.
- However, it is not linear because the term [tex]\(3x^2\)[/tex] is of degree 2.
4. Option 4: [tex]\(1 - 2x\)[/tex]
- This expression has two terms: [tex]\(1\)[/tex] and [tex]\(-2x\)[/tex].
- It is a binomial since it contains exactly two terms.
- It is linear because the degree of the variable [tex]\(x\)[/tex] is 1 (in the term [tex]\(-2x\)[/tex]).
Based on this analysis, the expression that is a linear binomial is option 4: [tex]\(1 - 2x\)[/tex].
Conclusion: The correct answer is option 4: [tex]\(1 - 2x\)[/tex].
