Chapter 2 Polynomials Ex 2.1

Question 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+ 2y
(v) x10+ y3+t50
Solution:
(i) 4x2 – 3x + 7 is an expression having only non-negative integral powers of x. So, it is a polynomial.
(ii) y2 +√2 is an expression having only non-negative integral power of y. So, it is a polynomial.
(iii) 3√t + √2 is an expression in which one term namely 3√t has rational power of f. So, it is not a polynomial.
(iv) y+ 2y is an expression in which one term namely 2y ⇒ i.e., 2y-1 has negative power of y. So, it is not a polynomial.
(v) x10 + y3 + t50 is an expression which has 3 variables.

Question 2.
Write the coefficients of x2 in each of the following
(i) 2 + x2 + x
(ii) 2 – x2 + x3

(iii) π2 x2 + x
(iv) √2 x – 1
Solution:
(i)
 The coefficient of x2 in 2 + x2 + x is 1.
(ii) The coefficient of x2 in 2 – x2 + x3 is – 1.
(iii) The coefficient of x2 in π2 x2+ x is π2 .
(iv) The coefficient of x2 in 2 x -1 is 0.

Question 3.
Give one example each of a binomial of degree 35, and of a monomial of degree 100.
Solution:
(i)
 y35 + 2 is a binomial of degree 35.
(ii) y100 is a monomial of degree 100.

Question 4.
Write the degree of each of the following polynomials.

(i) 5x3+4x2 + 7x
(ii) 4 – y2
(iii) 5f – √7

(iv) 3
Solution:
(i) In a polynomial 5x3 + 4x2 + 7x, the highest power of variable x is 3, hence degree of polynomial is 3.
(ii) In a polynomial 4 – y2, the highest power of variable y = 2, hence degree of polynomial is 2.
(iii) In a polynomial 5t – √7 , the highest power of variable t = 1, hence the degree of polynomial is 1.
(iv) In a polynomial 3, the highest power of variable y = 0, hence the degree of polynomial is 0.

Question 5.
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:
(i) The degree of polynomial x2 + 2 is 2, hence it is a quadratic polynomial.
(ii) The degree of polynomial x – x3 is 3, hence it is a cubic polynomial.
(iii) The degree of polynomial y + y2 + 4 is 2, hence it is a quadratic polynomial.
(iv) The degree of polynomial 1 + x is 1, hence it is a linear polynomial.
(v) The degree of polynomial 3t is 1, hence it a linear polynomial.
(vi) The degree of polynomial r2 is 2, hence it is a quadratic polynomial.
(vii) The degree of polynomial 7x3 is 3, hence it is a cubic polynomial.