Question

Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any category?
(i) x + y
(ii) 1000
(iii) x + x² + x³ + 4y⁴
(iv) 7 + a + 5b
(v) 2b − 3b²
(vi) 2y − 3y² + 4y³
(vii) 5x − 4y + 3x
(viii) 4a − 15a²
(ix) xy + yz + zt + tx
(x) pqr
(xi) p²q + pq²
(xii) 2p + 2q

Answer 1

Definitions:

A polynomial is monomial if it has exactly one term. It is called binomial if it has exactly two non-zero terms. A polynomial ​is a trinomial if it has exactly three non-zero terms.

(i) The polynomial $x+y$ has exactly two non zero terms , i.e.,​ x and y. Therefore, it is a binomial.
(ii) The polynomial 1000 has exactly one term, i.e., 1000. Therefore, it is a monomial.
(iii) The polynomial $x+x^2+x^3+x^4$ has exactly four terms, i.e.,​ $x,x^2,x^3\mathrm{and}{x}^4$. Therefore, it doesn't belong to any of the categories.
(iv) The polynomial $7+a+5b$ has exactly three terms, i.e., 7, a and 5b. Therefore, it is a trinomial.
(v) The polynomial $2b-3b^2$ has exactly two terms, i.e.,​ 2b and $-3b^2$. Therefore, it is a binomial.
(vi) The polynomial $2y-3y^2+4y^3$ has exactly three terms, i.e.,​ 2y, $-3y^2$ and $4y^3$. Therefore, it is a trinomial.
(vii) The polynomial $5x-4y+3x$ has exactly three terms, i.e.,​ 5x, $-$4y and 3x. Therefore, it is a trinomial.
(viii) The polynomial $4a-15a^2$ has exactly two terms, i.e., 4a and $-15a^2$. Therefore, it is a binomial.
(ix) The polynomial $xy+yz+zt+tx$ has exactly four terms xy, yz, zt and tx. Therefore, it doesn't belong to any of the categories.
(x) The polynomial pqr has exactly one term, i.e., pqr. Therefore, it is a monomial.
(xi) The polynomial $p^{2}q+p{q}^2$ has exactly two terms, i.e.,​ $p^{2}q$ and $p{q}^2$. Therefore, it is a binomial.
(xi) The polynomial $2p+2q$ has two terms, i.e.,​ 2p and 2q. Therefore, it is a binomial.