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  • Classify the following polynomials as polynomials in one variable, two variables etc. (i) x^{2}+x+1 (ii) y^{2}-5y (iii)xy+yz+zx (iv) x^{2}-2xy+y^{2}+1

Classify the following polynomials as polynomials in one variable, two variables etc.

            (i) x^{2}+x+1

            (ii) y^{2}-5y

            (iii) xy+yz+zx

            (iv) x^{2}-2xy+y^{2}+1

Answers (1)

(i) One Variable

 (ii) One Variable

(iii) Three Variables

(iv) Two Variables

Solution

In mathematics, a variable is a symbol whose role is to act as a substitute for a changing quantity or expression. It is often used to represent an arbitrary element.                                   

For example: - x, y, z etc.

(i) Here, x^{2}+x+1 is a one variable polynomial, because it contains only one variable,

i.e., x

(ii) y^{2}-5y

Here, y^{2}-5y is a one variable polynomial, because it contains only one variable,

i.e., y

 (iii) xy+yz+zx

Here, xy+yz+zx is three variable polynomial, because it contains three variables

i.e., x, y and z

(iv) x^{2}-2xy+y^{2}+1

Here, x^{2}-2xy+y^{2}+1 is two variable polynomials, because it contains two variables,

i.e., x and y

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