Linear Polynomials

The linear polynomial represents the foundation of understanding the linear relationship in the newly created maths syllabus for class nine NCERT. To comprehend this and apply it correctly to the growth/decay model, the students will develop analytical skills that will help them succeed in higher-order maths and problem-solving.

Regularly practicing the NCERT exercises, developing models of things they see every day, practicing plotting graphs will help keep this chapter exciting and successful on the CBSE exam. You will lay down a good foundation with this chapter for when you move on to the next chapter, which will be linear equations in two variables.

1.0Introduction to Linear Polynomials

Linear polynomials are polynomials whose degree equals one and which can therefore have a maximum of one exponent for each variable used in the polynomial.

The general form of a linear polynomial in one variable is: ax+b

Where:

a and b are real numbers,
a≠0 (otherwise, it becomes a constant),
x is the variable.

Examples: 2x+3, −x+7, 5z−6

All of these are linear polynomials because the highest power of their respective variables (x, y, z ) is 1

2.0Properties of Linear Polynomials

Degree: Always 1 (e.g., x¹)
One variable: Usually x, y, or z
Graph: The graph of a linear polynomial is always a straight line.
Number of zeros: A linear polynomial has exactly one zero (root).

3.0Solved Examples and Real-Life Applications

Question: Which of the following are linear polynomials?

(a) x²+4
(b) 3x+2
(c) 7
(d) 5x

Solution:

(a) x2+4 – Not linear (degree is 2)
(b) 3x+2 – Linear polynomial (degree is 1)
(c) 7 – Not linear (degree is 0, it’s a constant polynomial)
(d) 5x – Linear polynomial (degree is 1)

Question: Find the zero (root) of the linear polynomial f(x)=2x−6.

Solution: Set f(x)=0:

2x−6=0

2x=6

x=3

So, the zero is x=3.

Question: Suppose the total cost C (in rupees) of buying x movie tickets at ₹150 each is represented by the linear polynomial: C(x)=150x. If you buy 4 tickets, what is the total cost?

Solution:

C(4)=150×4=₹600

This shows how linear polynomials can represent real-world situations

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Linear Polynomials

The linear polynomial represents the foundation of understanding the linear relationship in the newly created maths syllabus for class nine NCERT. To comprehend this and apply it correctly to the growth/decay model, the students will develop analytical skills that will help them succeed in higher-order maths and problem-solving.

Regularly practicing the NCERT exercises, developing models of things they see every day, practicing plotting graphs will help keep this chapter exciting and successful on the CBSE exam. You will lay down a good foundation with this chapter for when you move on to the next chapter, which will be linear equations in two variables.

1.0Introduction to Linear Polynomials

Linear polynomials are polynomials whose degree equals one and which can therefore have a maximum of one exponent for each variable used in the polynomial.

The general form of a linear polynomial in one variable is: ax+b

Where:

a and b are real numbers,
a≠0 (otherwise, it becomes a constant),
x is the variable.

Examples: 2x+3, −x+7, 5z−6

All of these are linear polynomials because the highest power of their respective variables (x, y, z ) is 1

2.0Properties of Linear Polynomials

Degree: Always 1 (e.g., x¹)
One variable: Usually x, y, or z
Graph: The graph of a linear polynomial is always a straight line.
Number of zeros: A linear polynomial has exactly one zero (root).

3.0Solved Examples and Real-Life Applications

Question: Which of the following are linear polynomials?

(a) x²+4
(b) 3x+2
(c) 7
(d) 5x

Solution:

(a) x2+4 – Not linear (degree is 2)
(b) 3x+2 – Linear polynomial (degree is 1)
(c) 7 – Not linear (degree is 0, it’s a constant polynomial)
(d) 5x – Linear polynomial (degree is 1)

Question: Find the zero (root) of the linear polynomial f(x)=2x−6.

Solution: Set f(x)=0:

2x−6=0

2x=6

x=3

So, the zero is x=3.

Question: Suppose the total cost C (in rupees) of buying x movie tickets at ₹150 each is represented by the linear polynomial: C(x)=150x. If you buy 4 tickets, what is the total cost?

Solution:

C(4)=150×4=₹600

This shows how linear polynomials can represent real-world situations

Frequently Asked Questions

Join ALLEN!

(Session 2026 - 27)

Name

Mobile Number

Class

Choose class

Goal

Choose your goal

Preferred Programs

Preferred Mode

State

Choose State

I agree to

I authorise ALLEN Career Institute Pvt Ltd to send me regular updates via Phone calls, Whatsapp, SMS, Robocalls (Automated Calls), Emails, or on postal address.

Linear Polynomials

1.0Introduction to Linear Polynomials

2.0Properties of Linear Polynomials

3.0Solved Examples and Real-Life Applications

On this page

Frequently Asked Questions

What is a linear polynomial?

How many zeros does a linear polynomial have?

Can a linear polynomial have more than one variable?

What is the graph of a linear polynomial?

What is the importance of linear polynomials in real life?

Is x² + 1 a Linear Polynomial?

Join ALLEN!

Linear Polynomials

1.0Introduction to Linear Polynomials

2.0Properties of Linear Polynomials

3.0Solved Examples and Real-Life Applications

On this page

Frequently Asked Questions

What is a linear polynomial?

How many zeros does a linear polynomial have?

Can a linear polynomial have more than one variable?

What is the graph of a linear polynomial?

What is the importance of linear polynomials in real life?

Is x² + 1 a Linear Polynomial?

Join ALLEN!