Question

Classify the following polynomials as polynomials in one-variable, two variable etc:
(i) x²-xy+7y² (ii) x²-2tx+7y²-x+t
(iii) t³-3t²+4t-5 (iv) xy + yz + zx

Answer 1

(i) Given expression is x² - xy + 7y²  

Here, expression is in two variables and all powers of variables are non-negative integers.

Hence, it is a two variable polynomial.

 

(ii) Mistake in the question :

Given expression is x² - 2tx + 7t² - x + t

Here, expression is in two variables and all powers of variables are non-negative integers.

Hence, it is a two variable polynomial.

 

 

(iii) Given expression is t³ - 3t² + 4t - 5  

Here, expression is in one variable and all powers of variables are non-negative integers.

Hence, it is a one variable polynomial.

 

(iv) Given expression is xy + yz + zx

Here, expression is in three variables and all powers of variables are non-negative integers.

Hence, it is a three variable polynomial.

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Similar questions :

Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.

(i) 4x^2 - 3x + 7

(ii) y^2 + 2^(1/2)

(iii) 3.t^(1/2) + t.2^(1/2)

(iv) y + 2/y

(v) x^10 + y^3 + t^50

 

Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer:

(i) 3x²-4x+15

(ii) y²+2√3

(iii) 3+√x + √2x

(iv) x- 4/x

(v) x¹²+y3+t⁵⁰

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Answer 2

(i) x²-xy+7y²

Number of variables: x, y

Thus, its a two variable polynomial

(ii) x²-2tx+7y²-x+t

Number of variables: x, t

Thus, its a two variable polynomial

(iii) t³-3t²+4t-5

Number of variables: t

Thus, its a one variable polynomial

(iv) xy + yz + zx

Number of variables: x, y, z

Thus, its a three variable polynomial