# Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories?

x + y, 1000, x + x^{2} + x^{3} + x^{4}, 7 + y + 5x, 2y - 3y^{2}, 2y - 3y^{2} + 4y^{3}, 5x - 4y + 3xy, 4z - 15z^{2}, ab + bc + cd + da, pqr, p^{2}q + pq^{2}, 2p + 2q

**Solution:**

An expression containing, one or more terms with a non-zero coefficient (with variables having non-negative integers as exponents) is called a polynomial.A polynomial may contain any number of terms, one or more than one.

- An expression that contains only one term in the most simplified form is called a monomial
- An expression that contains two terms in the most simplified form is called a binomial
- An expression containing three terms in the most simplified form is a trinomial and so on.

The given expressions are classified as follows,

Monomials: 1000, pqr

Binomials: x + y, 2y - 3y^{2}, 4z - 15z^{2}, p^{2}q + pq^{2}, 2p + 2q

Trinomials: 7 + y + 5x, 2y - 3y^{2} + 4y^{3}, 5x - 4y + 3xy

Polynomials that do not fit in any of these categories are: x + x^{2} + x^{3} + x^{4}, ab + bc + cd + da

**Video Solution:**

## Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories? x + y, 1000, x + x² + x³ + x⁴, 7 + y + 5x, 2y - 3y², 2y - 3y² + 4y³, 5x - 4y + 3xy, 4z - 15z², ab + bc + cd + da, pqr, p²q + pq², 2p + 2q

### Maths NCERT Solutions Class 8 - Chapter 9 Exercise 9.1 Question 2

**Summary:**

The given polynomials x + y, 1000, x + x^{2} + x^{3} + x^{4}, 7 + y + 5x, 2y - 3y^{2}, 2 y - 3y^{2} + 4 y^{3}, 5x - 4 y + 3xy, 4z - 15z^{2}, ab + bc + cd + da, pqr, p^{2}q + pq^{2}, 2p + 2q are classified as: Monomials: 1000, pqr, Binomials: x + y, 2y - 3y^{2}, 4z - 15z^{2}, p^{2}q + pq^{2}, 2p + 2q, Trinomials: 7 + y + 5x, 2y - 3y^{2} + 4y^{3}, 5x - 4y + 3xy, Polynomials that do not fit in any of these categories are x + x^{2} + x^{3} + x^{4}, ab + bc + cd + da