Chapter 6 Factorisation of Algebraic Expressions RD Sharma Solutions Exercise 6.1 Class 9 Maths
Chapter Name  RD Sharma Chapter 6 Factorisation of Polynomials Exercise 6.1 
Book Name  RD Sharma Mathematics for Class 10 
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Related Study  NCERT Solutions for Class 10 Maths 
Exercise 6.1 Solutions
1. Which of the following expressions are polynomials in one variable and which are not ?
State reasons for your answer :
(i) 3x^{2}  4x + 15
(ii) y^{2} + 2√3
(iii) 3√x + √2x
(iv) x  4/x
(v) x^{12} + y^{3} + t^{50}
Solution
(i) 3x^{2}  4x + 15 is a polynomial of one variable x.
(ii) y^{2} + 2√3 is a polynomial of one variable y.
(iii) 3√x + √2x is not a polynomial as the exponents of 3√x is not a positive integer.
(iv) x  4/x is not a polynomial as the exponent of 4/x is not a positive integer.
(v) x^{12} + y^{3} + t^{50} is a polynomial of three variables x, y, t.
2. Write the coefficient of x^{2} in each of the following:
(i) 17  2x + 7x^{2}
(ii) 9  12x + x^{3}
(iii) Ï€/6 x^{2}  3x + 4
(iv) √x  7
Solution
Coefficient of x^{2} in
(i) 17  2x + 7x^{2} is 7
(ii) 9  12x + x^{3} is 0
(iii) Ï€/6 x^{2}  3x + 4 is Ï€/6
(iv) √x  7 is 0
3. Write the degree of each of the following polynomials :
(i) 7x^{3} + 4x^{2}  3x + 12
(ii) 12  x + 2x^{3}
(iii) 5y  √2
(iv) 7 = 7 × x°
(v) 0
Solution
Degree of polynomial
(i) 7x^{3} + 4x^{2}  3x + 12 is 3
(ii) 12  x + 2x^{3} is 3
(iii) 5y  √2 is 1
(iv) 7 = 7 × x° is 0
(v) 0 is undefined.
4. Classify the following polynomials as linear, quadratic, cubic and biquadratic polynomials:
(i) x + x^{2} + 4
(ii) 3x  2
(iii) 2x + x^{2}
(iv) 3y
(v) t^{2} + 1
(vi) 7t^{4} + 4t^{3} + 3t  2
Solution
Given polynomial
(i) x + x^{2} + 4 is quadratic as degree of polynomial is 2.
(ii) 3x  2 linear as degree of polynomial is 1.
(iii) 2x + x^{2} is quadratic as degree of polynomial is 2.
(iv) 3y is linear as degree of polynomial is 2.
(v) t^{2} + 1 is quadratic as degree of polynomial is 2.
(vi) 7t^{4} + 4t^{3} + 3t  2 is bi quadratic as degree of polynomial is 4.
5. Classify the following polynomials as polynomials is one  variable, two variables etc:
(i) x^{2}  xy + 7y^{2}
(ii) x^{2}  2tx + 7t^{2}  x + t
(iii) t^{3}  3t^{2} + 4t  5
(iv) xy + yz + zx
Solution
(i) x^{2}  xy + 7y^{2} is a polynomial in two variables x, y.
(ii) x^{2}  2tx + 7t^{2}  x + t is a polynomial in 2 variables x, t.
(iii) t^{3}  3t^{2} + 4t  5 is a polynomial in 1 variables t.
(iv) xy + yz + zx is a polynomial in 3 variables x, y, z.
6. Identify polynomials in the following:
(i) f(x) = 4x^{2}  x^{2}  3x + 7
(ii) g(x) = 2x^{3}  3x^{2} + √x  1
(iii) p(x) = 2/3 x^{2}  7/4 x + 9.
(iv) q(x) = 2x^{2}  3x + 4/x + 2
(v) h(x) = x^{4}  x^{3/2} + x  1
(vi) f(x) = 2 + 3/x + 4x
Solution
(i) f(x) = 4x^{2}  x^{2}  3x + 7 is a polynomial
(ii) g(x) = 2x^{3}  3x^{2} + √x  1 is not a polynomial as exponent of x in √x is not a positive integer.
(iii) p(x) = 2/3 x^{2}  7/4 x + 9. is a polynomial as all the exponents are positive integers.
(iv) q(x) = 2x^{2}  3x + 4/x + 2 is not a polynomial as exponent of x in 4/x is not a positive integer.
(v) h(x) = x^{4}  x^{3/2} + x  1 is not a polynomial as exponent of x in  x^{3/2} is not a positive integer.
(vi) f(x) = 2 + 3/x + 4x is not a polynomial as exponent of x in 3/x is not a positive integer.
7. Identify constant, linear, quadratic and cubic polynomials from the following polynomials:
(i) f(x) = 0
(ii) g(x) = 2x^{3}  7x + 4
(iii) h(x) = 3x + 1/2
(iv) p(x) = 2x^{3}  x + 4
(v) q(x) = 4x + 3
(vi) r(x) = 3x^{2} + 4x^{2} + 5x  7
Solution
Given polynomial
(i) f(x) = 0 is a constant polynomial as 0 is a constant
(ii) g(x) = 2x^{3}  7x + 4 is a cubic polynomial as degree of the polynomial is 3.
(iii) h(x) = 3x + 1/2 is a linear polynomial as degree of the polynomial is 1.
(iv) p(x) = 2x^{3}  x + 4 is a quadratic as the degree of the polynomial is 2.
(v) q(x) = 4x + 3 is a linear polynomial as the degree of the polynomial is 1.
(vi) r(x) = 3x^{2} + 4x^{2} + 5x  7 is a cubic polynomial as the degree is 3.
8. Give one example each of a binomial of degree 35, and of a monomial of degree 100.
Solution
Example of a binomial with degree 35 is 7x^{35}  5.
Example of a monomial with degree 100 is 2t^{100}