# Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any category?(i) $x+y$(ii) $1000$(iii) $x + x^2 + x^3 + x^4$(iv) $7 + a + 5b$(v) $2b – 3 b^2$(vi) $2y – 3y^2 +4y^3$(vii) $5x – 4y + 3x$(viii) $4a – 15a^2$(ix) $xy+yz + zt + tx$(x)$pqr$(xi) $p^2q + pq^2$(xii)$2p + 2q$

#### Complete Python Prime Pack for 2023

9 Courses     2 eBooks

#### Artificial Intelligence & Machine Learning Prime Pack

6 Courses     1 eBooks

#### Java Prime Pack 2023

8 Courses     2 eBooks

To do:

We have to classify the given polynomial as monomials, binomials, trinomials.

Solution:

Monomials: Polynomials having only one term are known as monomials.

Binomials: A binomial is a polynomial that is the sum of two terms.

Trinomial: A trinomial is a polynomial consisting of three terms.

(i) In the given polynomial there are two terms($x,y$).

Therefore, the given polynomial is a binomial.

(ii) In the given polynomial there is one term($1000$).

Therefore, the given polynomial is a monomial.

(iii) In the given polynomial there are four terms($x, x^2, x^3, x^4$).

Therefore, the given polynomial does not fit in any category.

(iv) In the given polynomial there are three terms($7, a, 5b$).

Therefore, the given polynomial is a trinomial.

(v) In the given polynomial there are two terms($2b, - 3b^2$).

Therefore, the given polynomial is a binomial.

(vi) In the given polynomial there are three terms($2y, - 3y^2, 4y^3$).

Therefore, the given polynomial is a trinomial.

(vii) In the given polynomial there are three terms($5x, - 4y, 3x$).

Therefore, the given polynomial is a trinomial.

(viii) In the given polynomial there are two terms($4a, -15a^2$).

Therefore, the given polynomial is a binomial.

(ix) In the given polynomial there are four terms($xy, yz, zt, tx$).

Therefore, the given polynomial does not fit in any category.

(x) In the given polynomial there is one term($pqr$).

Therefore, the given polynomial is a monomial.

(xi) In the given polynomial there are two terms($p^2q, pq^2$ ).

Therefore, the given polynomial is a binomial.

(xii) In the given polynomial there are two terms($2p, 2 q$ ).

Therefore, the given polynomial is a binomial.

Updated on 10-Oct-2022 13:19:20