**Question 1. Identify the terms, their coefficients for each of the following expressions:**

**(i) 7x ^{2}yz – 5xy**

**(ii) x ^{2} + x + 1**

**(iii) 3x ^{2}y^{2} – 5x^{2}y^{2}z^{2} + z^{2}**

**(iv) 9 – ab + bc – ca**

**(v) a/2 + b/2 – ab**

**(vi) 0.2x – 0.3xy + 0.5y**

**Solution:**

(i) 7x^{2}yz – 5xyIn this expression there are two terms:

7x

^{2}yz and – 5xyThe coefficient of 7x

^{2}yz is 7The coefficient of –5xy is –5

(ii) x^{2}+ x + 1In this expression there are three terms:

x

^{2}, x and 1The coefficient of x

^{2 }is 1The coefficient of x is 1

The coefficient of 1 is 1

(iii)3x^{2}y^{2}– 5x^{2}y^{2}z^{2}+ z^{2}In this expression there are three terms:

3x

^{2}y, -5x^{2}y^{2}z^{2}and z^{2}The coefficient of 3x

^{2}y is 3The coefficient of -5x

^{2}y^{2}z^{2}is -5The coefficient of z

^{2}is 1

(iv) 9 – ab + bc – caIn this expression there are four terms:

9, -ab, bc and -ca

The coefficient of 9 is 9

The coefficient of -ab is -1

The coefficient of bc is 1

The coefficient of -ca is -1

(v) a/2 + b/2 – abIn this expression there are three terms:

a/2, b/2, and -ab

The coefficient of a/2 is 1/2

The coefficient of b/2 is 1/2

The coefficient of -ab is -1

(vi) 0.2x – 0.3xy + 0.5yIn this expression there are three terms:

0.2x, -0.3xy and 0.5y

The coefficient of 0.2x is 0.2

The coefficient of -0.3xy is -0.3

The coefficient of 0.5y is 0.5

**Question 2. 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**

**Solution:**

(i) x + yThe given expression contains two terms x and y

∴ It is Binomial

(ii) 1000The given expression contains one term 1000

∴ It is Monomial

(iii) x + x^{2 }+ x^{3 }+ x^{4}The given expression contains four terms

∴ It belongs to none of the categories

(iv) 7 + a + 5bThe given expression contains three terms

∴ It is Trinomial

(v) 2b – 3b^{2}The given expression contains two terms

∴ It is Binomial

(vi) 2y – 3y^{2 }+ 4y^{3}The given expression contains three terms

∴ It is Trinomial

(vii) 5x – 4y + 3xThe given expression contains three terms

∴ It is Trinomial

(viii) 4a – 15a^{2}The given expression contains two terms

∴ It is Binomial

(ix) xy + yz + zt + txThe given expression contains four terms

∴ It belongs to none of the categories

(x) pqrThe given expression contains one term

∴ It is Monomial

(xi) p^{2}q + pq^{2}The given expression contains two terms

∴ It is Binomial

(xii) 2p + 2qThe given expression contains two terms

∴ It is Binomial