RD Sharma Solutions for Class 9 Mathematics Chapter 6 Exercise 6.1 Factorization of Polynomials are provided here. Sometimes students get confused between the degree and coefficient of a polynomial. Let us have a look at the definition of a polynomial and some of its terms.
A polynomial is an expression with a combination of constants and variables.
The exponent of the highest degree term in a polynomial is known as its degree, whereas the coefficient of the leading term is called the leading coefficient.
In this exercise, students will learn a polynomial in one variable only.
To improve conceptual understanding, students can practise RD Sharma Solutions Class 9 Chapter 6.
RD Sharma Solutions Class 9 Factorization of Polynomials Ex 6.1
Access Answers to Maths RD Sharma Solutions for Class 9 Chapter 6 Factorization of Polynomials Exercise 6.1 Page Number 6.2
Exercise 6.1 Page No: 6.2
Question 1: Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer:
(i) 3x2 – 4x + 15
(ii) y2 + 2√3
(iii) 3√x + √2x
(iv) x – 4/x
(v) x12 + y3 + t50
Solution:
(i) 3x2 – 4x + 15
It is a polynomial of x.
(ii) y2 + 2√3
It is a polynomial of y.
(iii) 3√x + √2x
It is not a polynomial since the exponent of 3√x is a rational term.
(iv) x – 4/x
It is not a polynomial since the exponent of – 4/x is not a positive term.
(v) x12 + y3 + t50
It is a three variable polynomial, x, y and t.
Question 2: Write the coefficient of x2 in each of the following:
(i) 17 – 2x + 7x2
(ii) 9 – 12x + x3
(iii) ∏/6 x2 – 3x + 4
(iv) √3x – 7
Solution:
(i) 17 – 2x + 7x2
Coefficient of x2 = 7
(ii) 9 – 12x + x3
Coefficient of x2 =0
(iii) ∏/6 x2 – 3x + 4
Coefficient of x2 = ∏/6
(iv) √3x – 7
Coefficient of x2 = 0
Question 3: Write the degrees of each of the following polynomials:
(i) 7x3 + 4x2 – 3x + 12
(ii) 12 – x + 2x3
(iii) 5y – √2
(iv) 7
(v) 0
Solution:
As we know, degree is the highest power in the polynomial
(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 – √2 is 1
(iv) Degree of the polynomial 7 is 0
(v) Degree of the polynomial 0 is undefined.
Question 4: Classify the following polynomials as linear, quadratic, cubic and biquadratic polynomials:
(i) x + x2 + 4
(ii) 3x – 2
(iii) 2x + x2
(iv) 3y
(v) t2 + 1
(vi) 7t4 + 4t3 + 3t – 2
Solution:
(i) x + x2 + 4: It is a quadratic polynomial as its degree is 2.
(ii) 3x – 2 : It is a linear polynomial as its degree is 1.
(iii) 2x + x2: It is a quadratic polynomial as its degree is 2.
(iv) 3y: It is a linear polynomial as its degree is 1.
(v) t2+ 1: It is a quadratic polynomial as its degree is 2.
(vi) 7t4 + 4t3 + 3t – 2: It is a biquadratic polynomial as its degree is 4.
RD Sharma Solutions for Class 9 Maths Chapter 6 Factorization of Polynomials Exercise 6.1
RD Sharma Solutions for Class 9 Maths Chapter 6 Factorization of Polynomials Exercise 6.1 are based on the following topics and subtopics:
- Factorization of polynomials introduction
- Terms and coefficients
- Degree of a polynomial
- Constant polynomial
- Linear polynomial
- Quadratic polynomial
- Cubic polynomial
- Bi-quadratic polynomial
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