Question

Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories:
$x+y,1000,x+x^2+x^3+x^4,7+y+5x,2y-3y^2,$ $2y-3y^2+4y^3,5x-4y+3xy,4z-15z^2,$
$ab+bc+cd+da,pqr,p^{2}q+p{q}^2,2p+2q$

Answer 1

(i) Since, $x+y$ contains two terms. Therefore it is binomial.
(ii) Since, 1000 contains one term. Therefore it is monomial.
iii) Since, $x+x^2+x^3+x^4$ contains four terms. Therefore it is a polynomial and it does not fit in the above three categories
(iv) Since, $7+y+5x$ contains three terms. Therefore it is a trinomial.
(v) Since, $2y-3y^2$ contains two terms. Therefore it is a binomial.
vi) Since $2y-3y^2+4y^3$ contains three terms. Therefore it is trinomial.
(vii) Since, $5x-4y-3xy$ contains three terms. Therefore it is a trinomial.
(viii) Since, $4z-15z^2$ contains two terms. Therefore it is a binomial.
(ix) Since, $ab+bc+cd+da$ contains four terms. Therefore it is a polynomial and it does not fit in above three categories
(x) Since, $pqr$ contains one term. Therefore it is a monomial
(xi) Since, $p^{2}q+p{q}^2$ contains two terms. Therefore it is a binomial.
(xii) Since, $2p+2q$ contains two terms. Therefore it is a binomial.