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)$2p + 2q$

AcademicMathematicsNCERTClass 8

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.

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

Advertisements