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