[Maths Class Notes] on Polynomials Pdf for Exam

The meaning of Polynomials is ‘many terms’, and it consists of coefficients and variables. These coefficients can be added, subtracted, or multiplied for various mathematical operations. While this chapter imparts knowledge about important terms like factoring polynomials, studying through these notes will help you learn the concept right.

You will be able to solve the exercise questions and answer them correctly once you have thoroughly read these notes. Now ensure that your academic performance gets better with these quality notes covering the intricacies of Polynomials. 

Introducing Polynomials 

Every polynomial is said to have a constant, a variable, and an exponent. It may have more than one terms and the number of terms determine the type of polynomial it is. For instance, take x2 + 5x + 3 as a polynomial expression. Clearly, it has 3 terms and hence can be called a trinomial. Monomial, binomial, etc. are few other kinds of polynomials here. 

In case polynomials are classified depending upon their degree, they are segregated into – 

• Linear – Expressions having degree as 1. 

• Cubic – Expressions having degree as 3.

• Quadratic – Expressions having degree as 2.

Examples of Polynomial

1. x + y 

2. 25 

3. 2x + y + 5 

4. a + b + c + d 

5. x2 + x + 2 

6. x3 + y2 + 2x + 2 

The algebraic expression for writing polynomials is as follows – 

p (x) = a0xn + a1xn-1 + a2xn-2 + … an 

Where, a0, a1, … … … an denotes the real numbers and the value of n is a positive integer. 

Factor Theorem

Consider a polynomial p (x) with degree equal to or greater than one, where ‘a’ is any real number. Then, we can conclude, 

1. If p (a) is ‘0’, then (x – a) will be a factor of p (x). 

2. If (x – a) factorises p (x), then p (a) will be 0. 

Remainder Theorem 

Consider a polynomial q (x) with degree equal to or greater than one, where ‘a’ is any real number. Then, we can conclude, dividing polynomials q (x) by a linear polynomial (x – a), then its remainder should be q (a). 

Adding and Subtracting Polynomials 

You can also add or subtract polynomials. To do so, you must add the like terms together or subtract from like terms. 

For instance, take two polynomials, as shown below. 

3 x2 + 5x + 8, 

and 2 x2 – x – 2. 

Place the like terms together and proceed to add. 

3 x2 + 2 x2 + 5x – x + 8 – 2 

Add the like terms together to get

(3 + 2) x2 + (5 – 1) x + (8 – 2) 

5 x2 + 4 x + 6 

Similarly, you can add or subtract polynomial terms by placing the like terms together and adding them. 

In case of subtraction, consider these polynomials 3 x2 + 5x + 8 and 2 x2 – x – 2. 

Place the like terms together and proceed to subtract. 

3 x2 – 2 x2 + 5x + x + 8 + 2 

Add the like terms together to get this 

(3 – 2) x2 + (5 + 1) x + (8 + 2) 

x2 + 6 x + 10

Now that you are familiar with the idea of multiplying polynomials, you will be able to solve the exercise questions effortlessly. It is critical to learn the theoretical concept and the method so that you can solve mathematical questions quickly.

The quality notes prepared by our expert tutors are meant to help you learn the concepts in an easy manner. Now start preparing for your upcoming exam with our notes and always score high grades in the exam. Now you can also download our app for easier access to these materials.