Question

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) \(2b-3b^{2}\)

(vi) \(2y-3y^{2}+4y^{3}\)

(vii) 5x-4y+3x

(viii) \(4a-15a^{2}\)

(ix) xy+yz+zt+tx

(x) pqr

(xi) \(p^{2}q+pq^{2}\)

(xii) 2p+2q

Answer 1

(i) x+y

This expression contains two terms x and y

So, it is called ‘Binomial’

(ii) 1000

It contains one term 1000

So, it is called monomial

(iii) \(x+x^{2}+x^{3}+x^{4}\)

It contains four terms

So, it is not a monomial, binomial and trinomial

(iv) 7+a+5b

It contains three terms

So, it is called trinomial

(v) \(2b-3b^{2}\)

It contains two terms

So, it is called binomial

(vi) \(2y-3y^{2}+4y^{3}\)

It contains three terms

So, it is called trinomial

(vii) 5x-4y+3x

8x – 4y

It contains two terms

So, it is called binomial

(viii) \(4a-15a^{2}\)

It contains two terms

So, it is called binomial

(ix) xy+yz+zt+tx

It contains four terms

So, it is not a monomial, binomial and trinomial

(x) pqr

It contains one term

So, it is called monomial

(xi) \(p^{2}q+pq^{2}\)

It contains two terms

So, it is called binomial

(xii) 2p+2q

It contains two terms

So, it is called monomial