Classify the following polynomials as monomials, binomials, trinomials

1.	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» (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

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»

(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