NCERT Solutions Class 9 Maths Chapter 2 Polynomials

Exercise 2.1

  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+\frac{2}{y}

    (v) x10+y3+t50
    Sol:- (i) 4x2–3x+7 is a polynomial in one variable. The equation 4x2–3x+7 can be written as 4x2–3x1+7x0 and since x is the only variable in the given equation and the powers of x (i.e., 2, 1 and 0) are whole numbers.
    (ii) y2+2 is a polynomial in one variable. The equation y2+√2 can be written as y2+2y0 Since y is the only variable in the given equation and the powers of y (i.e., 2 and 0) are whole numbers.
    (iii) 3√t+t√2 is not a polynomial in one variable. The equation 3√t+t√2 can be written as 3t1/2+√2t though, t is the only variable in the given equation, the powers of t (i.e.,1/2) is not a whole number.
    (iv) y+\frac{2}{y} is not a polynomial in one variable. The equation y+2/y an be written as y+2y-1 though, is the only variable in the given equation, the powers of y (i.e.,-1) is not a whole number.
    (v) x10+y3+t50  is not a polynomial in one variable. Here, in the equation x10+y3+t50 though, the powers, 10, 3, 50, are whole numbers, there are 3 variables used in the expression x10+y3+t50.
  2. Write the coefficients of x2 in each of the following:
    (i) 2+x2+x
    (ii) 2-x2+x3
    (iii) \frac{\pi }{2}x2+x
    (iv) √2x-1

    Sol:- (i) The coefficient of xin 2+x2+x is 1
    (ii) The coefficient of xin 2–x2+xis -1.
    (iii) The coefficient of xin \frac{\pi }{2}x2+x is \frac{\pi }{2} .
    (iv) The coefficient of xin √2x-1 is 0.
  3. Give one example each of a binomial of degree 35, and of a monomial of degree 100.
    Sol:- Binomial of degree 35: A polynomial having two terms and the highest degree 35 is called a binomial of degree 35. Eg.,  3x35+5.
    Monomial of degree 100: A polynomial having one term and the highest degree 100 is called a monomial of degree 100. Eg.,  4x100.
  4. Write the degree of each of the following polynomials:
    (i) 5x3+4x2+7x
    (ii) 4 – y2
    (iii) 5t –√7
    (iv) 3

    Ans:- (i) The degree of 5x3+4x2+7x is 3 as 3 is the highest power of x in the equation.
    (ii) The degree of 4–y2 is 2 as 2 is the highest power of y in the equation.
    (iii) The degree of 5t–√7 is 1 as 1 is the highest power of y in the equation.
    (iv) The degree of 3 is 0.
  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

    Sol:- (i) The highest power of x2+x is 2
    So, x2+x is a quadratic polynomial.
    (ii) The highest power of x–xis 3
    So, x–x3 is a cubic polynomial.
    (iii) The highest power of y+y2+4 is 2
    So,  y+y2+4is a quadratic polynomial.
    (iv) The highest power of 1+x is 1
    So, 1+x is a linear polynomial.
    (v) The highest power of 3t is 1
    So, 3t is a linear polynomial.
    (vi) The highest power of ris 2
    So,  r2is a quadratic polynomial.
    (vii) The highest power of 7xis 3
    So,  7x3 is a cubic polynomial.
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