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

(i) 4x2 - 3x + 7 (ii) y2 + 2 (iii) 3t + t2

(iv) y + 2y (v) x10 + y3 + t50

Solution:

  1. 4x2 - 3x + 7: This is an expression with only one variable x with +ve integer powers. Hence, this is a polynomial in one variable.

  2. y2 + 2: This is an expression with only one variable y with +ve integer powers. Hence, this is a polynomial in one variable.

  3. 3t + t2: This is an expression with only one variable t but one of the powers of t is 12 (in 3t), which is not +ve integer. Hence, this is not a polynomial.

  4. y + 2y = y + 2y-1: This is an expression with only one variable y but one of the powers of y is -1, which is not +ve integer. Hence, this is not a polynomial.

  5. x10 + y3 + t50:There are three variable x, y and t, hence, this is not a polynomial in one variable.