# 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

**☛ Check: **NCERT Solutions for Class 8 Maths Chapter 9

**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

**☛ Related Questions:**

- Identify the terms, their coefficients for each of the following expressions. (i) 5xyz2 - 3zy (ii) 1 + x + x2 (iii) 4x2y2 - 4x2y2z2 + z2 (iv) 3 - pq + qr - rp (v) x + y - xy (vi) 0.3a - 0.6ab + 0.5b
- Add the following. (i) ab - bc, bc - ca, ca - ab (ii) a - b + ab, b - c + bc , c - a + ac (iii) 2 p2q2 - 3 pq + 4, 5 + 7 pq - 3 p2q2 (iv) l2 + m2, m2 + n2, n2 + l2, 2lm + 2mn + 2nl
- (a) Subtract 4a - 7ab + 3b + 12 from 12a - 9ab + 5b - 3 (b) Subtract 3xy + 5yz - 7zx from 5xy - 2 yz - 2zx +10xyz (c) Subtract 4p2q - 3pq + 5pq2 - 8p + 7q - 10 from 18 - 3p - 11q + 5 pq - 2 pq2 + 5 p2q
- Find the product of the following pairs of monomials. (i) 4,7 p (ii ) -4p, 7p (iii ) -4p, 7pq (iv) 4p3, 3p (v) 4p, 0

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