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.

Answer:

Polynomials are algebraic expressions that consist of variables and coefficients. Polynomials are of 3 different types and are classified based on the number of terms in it. The three types of polynomials are

Monomial

A monomial is an expression that contains only one term. For an expression to be a monomial, the single term should be a non-zero term.

Binomial

A binomial is a polynomial expression that contains exactly two terms. A binomial can be considered as a sum or difference between two or more monomials.

Trinomial

A trinomial is an expression that is composed of exactly three terms.

Monomial

(one term)

Binomial

(Two terms)

Trinomial

(Three terms)

Polynomial, and it does not fit in listed three categories

1000

x+y

2y – 3y2 + 4y3

x + x2 + x3 + x4

pqr

2y – 3y2

5x – 4y + 3xy

ab + bc + cd + da

4z – 15z2

7 + y + 5x

p2q + pq2

2p + 2q

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