Identify monomials, binomials and trinomials from the following algebraic expressions :
`1+x +x^(2)+x^(3)+x^(4)`

Answer

To solve the problem of identifying monomials, binomials, and trinomials from the given algebraic expression \(1 + x + x^2 + x^3 + x^4\), we can follow these steps:

### Step 1: Understand the Definitions
- **Monomial**: An algebraic expression with only one term.
- **Binomial**: An algebraic expression with exactly two terms.
- **Trinomial**: An algebraic expression with exactly three terms.

### Step 2: Identify the Terms in the Expression
The given expression is:
\[ 1 + x + x^2 + x^3 + x^4 \]

Let's break it down:
- The terms in this expression are:
1. \(1\)
2. \(x\)
3. \(x^2\)
4. \(x^3\)
5. \(x^4\)

### Step 3: Count the Number of Terms
In total, we have **five terms** in the expression.

### Step 4: Classify the Expression
Since the expression has five terms, it does not fit the definitions of monomial, binomial, or trinomial. Therefore, we can conclude that:
- This expression is neither a monomial, nor a binomial, nor a trinomial. It is simply a polynomial with five terms.

### Final Answer
The expression \(1 + x + x^2 + x^3 + x^4\) is a polynomial with five terms.

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