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

Monomial

A monomial is an expression that contains only one term.

For an expression to be a monomial, the single term should be a non-zero term.

The monomials in the given data are as follows:

Monomial (One term)	Terms in the monomial
$1000$	Here we have only one term (i.e $1000$)
$pqr$	Here we have only one term (i.e $pqr$)

Binomial

A binomial is a polynomial expression that contains exactly two terms.

A binomial can be considered as a sum or difference between two or more monomials.

The binomials in the given data are as follows:

Binomial (Two terms)	Terms in the binomial
$x+y$	Here we have two terms. They are $x,y$
$2y–3y^2$	Here we have two terms. They are $2y,-3y^2$
$4z–15z^2$	Here we have two terms. They are $4y,-15z^2$
$p^{2}q+p{q}^2$	Here we have two terms. They are $p^{2}q,p{q}^2$
$2p+2q$	Here we have two terms. They are $2p,2q$

Trinomial

A trinomial is an expression that is composed of exactly three terms.

The trinomials in the given data are as follows:

Trinomial(Three terms)	Terms in the trinomial
$2y–3y^2+4y^3$	Here we have three terms. They are $2y,–3y^2,4y^3$
$5x–4y+3xy$	Here we have three terms. They are $5x,–4y,3xy$
$7+y+5x$	Here we have three terms. They are $7,y,5x$

The expressions that are neither monomial, binomial nor trinomial are as follows

Polynomials that don't fall into any of the above category	Terms in the given polynomial
$x+x^2+x^3+x^4$	Here we have four terms (i.e $x,x^2,x^3,x^4$). Hence they don't fall into any of the above categories.
$ab+bc+cd+da$	Here we have four terms (i.e $ab,bc,cd,da$). Hence they don't fall into any of the above categories.