Class 9 Maths - GUJARAT
Linear Polynomials
In the Chapter 'Linear Polynomials' of Class 9 Mathematics under the Gujarat Secondary and Higher Secondary Education Board (GSEB), students explore algebraic expressions where the highest power of the variable is one. This chapter builds a strong foundation for coordinate geometry and linear equations in two variables. You will learn about the degree of polynomials, evaluating polynomials for specific values, finding zeroes of a polynomial, and applying the Remainder Theorem and Factor Theorem. Mastering these concepts is crucial for board exams as they form the backbone of higher-level algebra in Class 10.
Start Learning FreeKey Concepts
Degree of a Polynomial
The highest power of the variable in a polynomial is called its degree. For a linear polynomial, the degree is always 1.
Linear Polynomial
A polynomial of degree one, generally written in the standard form p(x) = ax + b, where 'a' and 'b' are real numbers and a ≠ 0.
Zero of a Polynomial
A real number 'k' is a zero of a polynomial p(x) if p(k) = 0. Geometrically, it is the x-coordinate where the graph of the polynomial intersects the x-axis.
Remainder Theorem
If p(x) is any polynomial of degree greater than or equal to one and it 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 p(a) = 0.
Important Formulas
Board Exam Info
In the Gujarat (GSEB) Class 9 Mathematics board-aligned exams, this chapter typically carries around 4 to 6 marks. Common question types include finding the zero of a given linear polynomial, testing whether a binomial is a factor of a polynomial using the Factor Theorem, and finding the remainder without actual division using the Remainder Theorem.
Frequently Asked Questions
What is the difference between a linear equation and a linear polynomial?
A linear polynomial is an algebraic expression like ax + b, whereas a linear equation includes an equality sign, such as ax + b = 0.
Can a linear polynomial have more than one zero?
No, a linear polynomial of the form ax + b always has exactly one and only one zero, which is x = -b/a.
How do I know if (x - a) is a factor of p(x)?
Substitute x = a into the polynomial p(x). If the resulting value p(a) equals zero, then (x - a) is a factor.
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