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Introduction to Linear Polynomials

NCERT Class 9 Maths • Chapter 2

Quick Answer

This Class 9 Maths chapter introduces polynomials, focusing on linear polynomials in one variable. Students learn terms, coefficients, degree, and zeroes of a polynomial, how to evaluate expressions, and how a linear polynomial of the form ax + b relates to a straight-line graph, laying the groundwork for algebra and equations.

↓ Free PDF, NCERT solutions, summary, key terms, FAQs below.

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Key Terms

Polynomial
An algebraic expression made of variables and constants combined using addition, subtraction, and multiplication with whole-number exponents.
Linear Polynomial
A polynomial of degree one, written in the form ax + b where a is not zero.
Degree of a Polynomial
The highest power of the variable in a polynomial; a linear polynomial has degree one.
Coefficient
The numerical factor multiplied with a variable in a term of a polynomial.
Constant Term
The term in a polynomial that has no variable, such as b in ax + b.
Zero of a Polynomial
A value of the variable for which the polynomial equals zero; for ax + b it is x = −b/a.
Variable
A symbol, usually a letter such as x, that represents an unknown or changing quantity in an expression.

Frequently Asked Questions

What is a linear polynomial in Class 9?▾

A linear polynomial is a polynomial of degree one, written in the general form ax + b, where a and b are constants and a is not zero. Its highest power of the variable is one, and its graph is always a straight line.

What is the degree of a polynomial?▾

The degree of a polynomial is the highest exponent of the variable present in it. For example, 3x + 5 has degree 1 (linear), while x² + 2x + 1 has degree 2 (quadratic). The degree tells us the type of polynomial.

How do you find the zero of a linear polynomial?▾

Set the polynomial equal to zero and solve for the variable. For a linear polynomial ax + b, solving ax + b = 0 gives x = −b/a. This value is the zero, where the graph crosses the x-axis.

What is the difference between a term and a coefficient?▾

A term is a single part of a polynomial separated by plus or minus signs, such as 3x or 5. A coefficient is the number multiplied with the variable in a term; in 3x the coefficient is 3.

How is a linear polynomial different from a linear equation?▾

A linear polynomial is an expression like ax + b that has a value depending on x. A linear equation sets a polynomial equal to a value, such as ax + b = 0, and is solved to find the unknown. The polynomial becomes an equation when an equals sign is added.

Can a constant be called a polynomial?▾

Yes. A non-zero constant such as 7 is a polynomial of degree zero, called a constant polynomial. The number 0 itself is the zero polynomial, whose degree is not defined.

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