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# 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) **$2b – 3 b^2$

**(vi)** $2y – 3y^2 +4y^3$

**(vii)** $5x – 4y + 3x$

**(viii)** $4a – 15a^2$

**(ix)** $xy+yz + zt + tx$

**(x)**$pqr$

**(xi)** $p^2q + pq^2$

**(xii**)$2p + 2q$

To do:

We have to classify the given polynomial as monomials, binomials, trinomials.

Solution:

**Monomials:** Polynomials having only one term are known as monomials.

**Binomials:** A binomial is a polynomial that is the sum of two terms.

**Trinomial: **A trinomial is a polynomial consisting of three terms.

(i) In the given polynomial there are two terms($x,y$).

Therefore, the given polynomial is a binomial.

(ii) In the given polynomial there is one term($1000$).

Therefore, the given polynomial is a monomial.

(iii) In the given polynomial there are four terms($x, x^2, x^3, x^4$).

Therefore, the given polynomial does not fit in any category.

(iv) In the given polynomial there are three terms($7, a, 5b$).

Therefore, the given polynomial is a trinomial.

(v) In the given polynomial there are two terms($2b, - 3b^2$).

Therefore, the given polynomial is a binomial.

(vi) In the given polynomial there are three terms($2y, - 3y^2, 4y^3$).

Therefore, the given polynomial is a trinomial.

(vii) In the given polynomial there are three terms($5x, - 4y, 3x$).

Therefore, the given polynomial is a trinomial.

(viii) In the given polynomial there are two terms($4a, -15a^2$).

Therefore, the given polynomial is a binomial.

(ix) In the given polynomial there are four terms($xy, yz, zt, tx$).

Therefore, the given polynomial does not fit in any category.

(x) In the given polynomial there is one term($pqr$).

Therefore, the given polynomial is a monomial.

(xi) In the given polynomial there are two terms($p^2q, pq^2$ ).

Therefore, the given polynomial is a binomial.

(xii) In the given polynomial there are two terms($2p, 2 q$ ).

Therefore, the given polynomial is a binomial.

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