# Polynomial – Exercise 2.1 – Class IX

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) 3√t + t√2

(iv) y + 2/y

(v)x10 +y3 +  t50

Solution:

(i)Polynomial in one variable, x

(ii)Polynomial in one variable, y

(iii) 3√t + t√2 is not  a  polynomial as power of t in √2t is  not a whole number

(iv) y + 2/y is not a polynomial as a power of  y  in 1/y = y-1  is not a whole number

(v) x10 +y3 +  t50 is not a polynomial with three variables x , y and t.

1. Write the coefficients of x2 in each of the following:

(i) 2+ x2 + x

(ii) 2 – x2 + x3

(iii) π/2 . x2 + x

(iv)√2x – 1

Solution:

(i) 2+ x2 + x, coefficient of x2 is 1

(ii) 2 – x2 + x3, coefficient of x2 is -1

(iii) π/2 . x2 + x, coefficient of x2 is π/2

(iv)√2x – 1, x2 is not there therefore there is no coefficient.

1. Give one example each of a binomial of degree 35 and of a monomial of degree 100

Solution:

Binomial of degree 35  can be a35 + 10

monomial of degree 100 can be x100

1. Write the degree of each of the following polynomials:

(i) 5x3 + 4x2+ 7

(ii)  4 – y2

(iii)   5t – √7

(iv)  3

Solution:

(i) 5x3 + 4x2+ 7, degree of a polynomial is 3 as x3 is the highest power.

(ii)  4 – y2, degree of a polynomial is 2 as x2 is the highest power.

(iii)   5t – √7, degree of a polynomial is 1 as x is the highest power.

(iv)  3, degree of a polynomial is 0 as x0 is the highest power.

1. Classify the following as linear, quadratic and cubic polynomials:

(i)x2 + x

(ii) x – x3

(iii)y + y2 + 4

(iv) 1 + x

(v) 3t

(vi) r2

(vii) 7x3

Solution:

(ii) x – x3, , is cubic

(iii)y + y2 + 4, is quadratic

(iv) 1 + x, is linear

(v) 3t, is linear