RD Sharma Chapter 6 Class 9 Maths Exercise 6.1 Solutions is based on the Factorization of Polynomials. A polynomial is an identity in which a unification of constants and variables. It is common to get confused between the degree and coefficient of a polynomial. So, the exponent of the highest degree number in a polynomial is called its degree, whereas the coefficient of the leading term is known as the leading coefficient.
Go down to the article to get more details about the Factorization of Polynomials. We have also attached the RD Sharma Chapter 6 Class 9 Maths Exercise 6.1 Solutions PDF for the students to do more and more practice on every type of question-related to this exercise. Moreover, the questions are taken from the CBSE Maths Book and RD Sharma of Class 9.
Download RD Sharma Chapter 6 Class 9 Maths Exercise 6.1 Solutions PDF
Solutions for Class 9 Maths Chapter 6 Factorization of Polynomials Exercise 6.1
Important Definitions RD Sharma Chapter 6 Class 9 Maths Exercise 6.1 Solutions
In this exercise, learners will get to know about the factorization of Polynomials 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
Factorization of Polynomials introduction
Factorization of Polynomials signifies a polynomial with coefficients in a provided area or the integers as the product of fundamental factors with coefficients in the corresponding domain. Polynomial factorization is one of the significant components of computer algebra operations.
Terms and Coefficients
Term
A term can be a number, product, a variable of two or more variables, or product of a number and a variable. An algebraic identity is formed by a separate term or by a group of terms.
For example, in the expression 6x + y, the two terms are 6x and y.
Coefficient
- A coefficient is an integer that is formulated along with a variable or multiplied by the variable.
For example, in the term 9p, 9 is the co-efficient.
- Those variables which do not carry any number with them have a coefficient of one.
For example, the term q has a coefficient of 1.
Degree of a Polynomial
A polynomial degree is the highest or the greatest power of a variable in a polynomial equalization. The degree symbolizes the highest exponential power in the polynomial (neglecting the coefficients).
For Example-
5x4 + 3x3+ 2 is a polynomial. Here 5x4, 3x3, 2 are the terms where 5x4 is a leading term and 2 is a constant term. The coefficients of the polynomial are 5 and 3.
The degree of a polynomial of 5x4 + 3x3+ 2 is 4.
Constant Polynomial
A constant polynomial is the likewise thing as a constant function. That is, a constant polynomial is a function of the form “p(x) = c” for any number c.
Constant polynomials are also known as degree 0 polynomials.
Linear Polynomial
A linear polynomial is some polynomial described by an equation of the form p(x) = ax + b where ‘a’ and ‘b’ are real numbers and a 0.
For example-
p(x) = 3 x 7 and q(x) = + are linear polynomials.
A linear polynomial is similar thing as a degree 1 polynomial.
Quadratic Polynomial
A Factorization of Algebraic Expression of the quadratic function is a polynomial of degree two (2) or just a quadratic. It is a polynomial function with one or more variables in which the highest-degree exponent is of the second degree.
Cubic Polynomial
A cubic polynomial is a polynomial of degree three (3), i.e., the highest term of the variable is three.
Bi-Quadratic Polynomial
A Biquadratic Polynomial is a type of quartic polynomial that only has terms of powers 4, 2, and 0.
Frequently Asked Questions (FAQs) of RD Sharma Chapter 6 Class 9 Maths Exercise 6.1 Solutions
Ques 1- What is an example of a quartic polynomial?
Ans- A polynomial of degree 4.
Examples-
- 3a4 – 2a3 + a2 + 8
- p4 + 1
- m3n + m2n2 + mn
Ques 2- What is the formula of the cubic polynomial?
Ans- The cubic formula shows us the roots of a cubic polynomial
The formula of Cubic Polynomial is-.
Ques 3- What does a quadratic polynomial look like?
Ans- A quadratic polynomial is a second-degree polynomial function.
The general form of a quadratic function is this: f (x) = px2 + qx + r where p, q, and r are real numbers, and a≠ 0.