## 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) 3x^{2} – 4x + 15,

(ii) y^{2} + 2\(\sqrt { 3 } \) are polynomial is one variable. Others are not polynomial or polynomials in one variable.

Question 2.

Write the coefficient of x^{2} in each of the following:

Solution:

Coefficient of x^{2},

in (i) is 7

in (ii) is 0 as there is no term of x^{2} i.e. 0 x^{2
}

Question 3.

Write the degrees of each of the following polynomials:

(i) 7x^{3} + 4x^{2} – 3x + 12

(ii) 12 – x + 2x^{3}

(iii) 5y – \(\sqrt { 2 } \)

(iv) 7

(v) 0

Solution:

(i) Degree of the polynomial 7x^{3} + 4x^{2} – 3x + 12 is 3

(ii) Degree of the polynomial 12 – x + 2x^{3} 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 + x^{2} + 4

(ii) 3x – 2

(iii) 2x + x^{2} [NCERT]

(iv) 3y

(v) t^{2} + 1

(v) 7t^{4} + 4t^{3} + 3t – 2

Solution:

(i) x + x^{2} + 4 It is a quadratic polynomial.

(ii) 3x – 2 : It is a linear polynomial.

(iii) 2x + x^{2}: It is a quadratic polynomial.

(iv) 3y It is a linear polynomial.

(v) t^{2}+ 1 It is a quadratic polynomial.

(vi) 7t^{4} + 4t^{3} + 3t – 2 It is a biquadratic polynomial.

Question 5.

Classify the following polynomials as polynomials in 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}: It is a polynomial in two j variables x, y.

(ii) x^{2} – 2tx + 7t^{2} – x + t: It is a polynomial in two variables in x, t.

(iii) t^{3} – 3t^{2} + 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) = 2x^{3} – 7x + 4 : It is a cubic polynomial.

(iii) h(x) = -3x + \(\frac { 1 }{ 2 }\) : It is a linear polynomial.

(iv) p(x) = 2x^{2} – x + 4 : It is a quadratic polynomial.

(v) q(x) = 4x + 3 : It is linear polynomial.

(vi) r(x) = 3x^{3} + 4x^{2} + 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 = 9x^{35} + 16

Example of a monomial of degree 100 = 2y^{100}

### RD Sharma class 9 maths Solutions Factorization of Polynomials Chapter 6 Exercise 6.1

RD Sharma class 9 maths Solutions Factorization of Polynomials Chapter 6 Exercise 6.1 Q 1.