Class 9 Maths - CBSE
Linear Polynomials
In the Class 9 CBSE chapter on Polynomials, students build upon algebraic expressions by studying polynomials in one variable, their degrees, and coefficients. This chapter introduces the foundational concept of zeroes of a polynomial, teaching you how to find where a polynomial evaluates to zero. You will also learn and apply the Remainder Theorem and Factor Theorem, which are powerful algebraic tools used to factorize polynomials efficiently. Mastering these topics is essential because polynomials form the absolute backbone of algebra, laying the groundwork for quadratic equations, coordinate geometry, and calculus in higher classes, and frequently appearing in CBSE board exams.
Start Learning FreeKey Concepts
Polynomial in One Variable
An algebraic expression consisting of variables and coefficients, involving only non-negative integer powers of the variable, such as p(x) = ax + b.
Degree of a Polynomial
The highest power of the variable in a polynomial. For a linear polynomial, the degree is always 1.
Zero of a Polynomial
A real number 'k' is a zero of a polynomial p(x) if p(k) = 0, which geometrically represents the x-intercept of the polynomial's graph.
Remainder Theorem
If a polynomial p(x) of degree greater than or equal to 1 is divided by a linear polynomial x - a, the remainder is equal to p(a).
Factor Theorem
If p(x) is a polynomial of degree n >= 1 and 'a' is any real number, then (x - a) is a factor of p(x) if and only if p(a) = 0.
Important Formulas
Board Exam Info
In the CBSE Class 9 Mathematics annual examination, the chapter on Polynomials carries approximately 6 to 8 marks. Questions typically range from 1-mark objective questions (identifying degrees or zeroes) and 2-mark short answers (evaluating values using the Remainder Theorem) to 3 or 4-mark long-answer questions involving the Factor Theorem and algebraic identities for factorization.
Frequently Asked Questions
What is the difference between a coefficient and a degree?
A coefficient is the numerical multiplier attached to a variable term (like 3 in 3x^2), whereas the degree is the highest exponent of the variable in the polynomial.
Can a polynomial have a negative or fractional exponent?
No, by definition, a polynomial can only have non-negative integer exponents (0, 1, 2, 3...) for its variables. Expressions with square roots of variables or variables in denominators are not polynomials.
How do I know whether to use the Remainder Theorem or actual division?
Use the Remainder Theorem when the question specifically asks for the remainder without requiring the quotient, as it saves time and prevents calculation errors.
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