Chapter 2 of Class 9 Maths Ganita Manjari Part 1 is Introduction to Linear Polynomials. It builds on earlier ideas of algebraic expressions to formally define polynomials, focusing on linear polynomials in one variable and their zeroes. These Class 9 Mathematics Chapter 2 solutions are also useful as quick revision notes before exams.
What Is a Polynomial?
A polynomial in one variable x is an algebraic expression of the form a₀ + a₁x + a₂x² + … + aₙxⁿ, where the exponents of x are whole numbers and the coefficients are real numbers. Based on the number of terms: a monomial has one term, a binomial has two, a trinomial has three.
Degree of a Polynomial
The degree is the highest power of the variable in the polynomial. A linear polynomial has degree 1 (e.g. 2x + 3); a quadratic polynomial has degree 2; a cubic polynomial has degree 3.
Zero of a Polynomial
A zero (or root) of a polynomial p(x) is a value of x for which p(x) = 0. A linear polynomial ax + b (a ≠ 0) has exactly one zero: x = −b/a.
Graph of a Linear Polynomial
The graph of a linear polynomial y = ax + b is always a straight line. The zero of the polynomial corresponds to the x-coordinate where this line crosses the x-axis.
Remainder and Factor Concepts (Introductory)
Evaluating a polynomial p(x) at x = a (i.e. finding p(a)) tells us the value of the polynomial at that point; if p(a) = 0, then (x − a) is a factor of the polynomial, and a is a zero of the polynomial.
Class 9 Mathematics Chapter 2 – Notes and Extra Questions
Along with these NCERT Solutions, students can also use the Class 9 Mathematics Chapter 2 Extra Questions and Class 9 Mathematics Chapter 2 Revision Notes for quick revision and extra practice.
