RD Sharma class 9 maths Solutions Factorization of Polynomials

RD Sharma Class 9 Solutions Chapter 6 Factorisation of Polynomials Ex 5.1

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

Solution:
(i) 3x² – 4x + 15,
(ii) y² + 2 $\sqrt { 3 }$ are polynomial is one variable. Others are not polynomial or polynomials in one variable.

Question 2.
Write the coefficient of x² in each of the following:

Solution:
Coefficient of x²,
in (i) is 7
in (ii) is 0 as there is no term of x² i.e. 0 x²

Question 3.
Write the degrees of each of the following polynomials:
(i) 7x³ + 4x² – 3x + 12
(ii) 12 – x + 2x³
(iii) 5y – $\sqrt { 2 }$
(iv) 7
(v) 0
Solution:
(i) Degree of the polynomial 7x³ + 4x² – 3x + 12 is 3
(ii) Degree of the polynomial 12 – x + 2x³ is 3
(iii) Degree of the polynomial 5y – $\sqrt { 2 }$ is 1
(iv) Degree of the polynomial 7 is 0
(v) Degree of the polynomial 0 is 0 undefined.

Question 4.
Classify the following polynomials as linear, quadratic, cubic and biquadratic polynomials:
(i) x + x² + 4
(ii) 3x – 2
(iii) 2x + x² [NCERT]
(iv) 3y
(v) t² + 1
(v) 7t⁴ + 4t³ + 3t – 2
Solution:
(i) x + x² + 4 It is a quadratic polynomial.
(ii) 3x – 2 : It is a linear polynomial.
(iii) 2x + x²: It is a quadratic polynomial.
(iv) 3y It is a linear polynomial.
(v) t²+ 1 It is a quadratic polynomial.
(vi) 7t⁴ + 4t³ + 3t – 2 It is a biquadratic polynomial.

Question 5.
Classify the following polynomials as polynomials in one-variable, two-variables etc.
(i) x²-xy +7y²
(ii) x² – 2tx + 7t² – x + t
(iii) t³ -3t² + 4t-5
(iv) xy + yz + zx
Solution:
(i) x² – xy + 7y²: It is a polynomial in two j variables x, y.
(ii) x² – 2tx + 7t² – x + t: It is a polynomial in two variables in x, t.
(iii) t³ – 3t² + 4t – 5 : It is a polynomial in one variable in t.
(iv) xy +yz + zx : It is a polynomial in 3 variables in x, y and

Question 6.
Identify polynomials in the following:

Solution:

Question 7.
Identify constant, linear, quadratic and cubic polynomials from the following polynomials:

Solution:
(i) f(x) = 0 : It is a constant polynomial as it has no variable.
(ii) g(x) = 2x³ – 7x + 4 : It is a cubic polynomial.
(iii) h(x) = -3x + $\frac { 1 }{ 2 }$ : It is a linear polynomial.
(iv) p(x) = 2x² – x + 4 : It is a quadratic polynomial.
(v) q(x) = 4x + 3 : It is linear polynomial.
(vi) r(x) = 3x³ + 4x² + 5x – 7 : It is a cubic polynomial.

Question 8.
Give one example each of a binomial of degree 35 and of a monomial of degree 100. [NCERT]
Solution:
Example of a binomial of degree 35 = 9x³⁵ + 16
Example of a monomial of degree 100 = 2y¹⁰⁰