Polynomials

Exercise 2.1 Part 1

Question 1: Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.

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

Answer: Since, the given expression has only one variable ‘x’, hence this is a polynomial in one variable.


(ii) `y^2 + sqrt2`

Answer: Since, the given expression has only one variable ‘y’, hence this is a polynomial in one variable.

(iii) `3sqrt\t + t\sqrt2`

Answer: Since, variable, ‘t’ in this expression exponent of variable is not a whole number. [Exponent of a variable in a polynomial must be a whole number. Expression with exponent of a variable in fraction is not considered as a polynomial.]


(iv) `y + 2/y`

Answer: Since, exponent of the variable is negative integer, and not a whole number, hence it cannot be considered a polynomial.

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

Answer: Since, given expression has three variables, i.e. x, y and t, so it is not a polynomial in one variable.

Question 2: Write the coefficients of x2 in each of the following:

(i) `2 + x^2 + x`

Answer: Given; `2 + x^2 + x`
Here, coefficient of `x^2 = 1`

(ii) `2 – x^2 + x^3`

Answer: Here, coefficient of `x^2 = 1`

(iii) `(π)/(2)\x^2 + x`

Answer: Here, coefficient of `x^2 = π/2`

(iv) `sqrt2x – 1`

Answer: Here, coefficient of `x^2 = 0`



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