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Polynomials

Punjab Board · Class 9 · Mathematics

Quick revision notes for Polynomials — Punjab Board Class 9 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

45 questions32 flashcards5 concepts

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A labeled diagram illustrating the general form of a polynomial, distinguishing between real and complex polynomials by highlighting the nature of coefficients and variables. Also includes the definit
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Key Topics to Revise

1

1. Polynomials in One Variable – Basic Concepts

  • A polynomial in one variable x is an expression of the form a_n·x^n + a_(n-1)·x^(n-1) + ... + a_1·x + a_0, where all exponents are whole numbers (0, 1, 2, 3, ...).
  • Each part of a polynomial separated by + or – signs is called a TERM.
  • The number multiplied with the variable in each term is called the COEFFICIENT.
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2. Zeroes of a Polynomial

  • The VALUE of a polynomial p(x) at x = a is found by substituting x = a in the expression. It is denoted p(a).
  • A ZERO of polynomial p(x) is a number 'c' such that p(c) = 0.
  • Finding a zero means solving the equation p(x) = 0.
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3. Remainder Theorem and Factor Theorem

  • REMAINDER THEOREM: When polynomial p(x) is divided by (x – a), the remainder is p(a). You do NOT need to perform long division to find the remainder!
  • FACTOR THEOREM: (x – a) is a factor of p(x) if and only if p(a) = 0.
  • The Factor Theorem is a special case of the Remainder Theorem (when remainder = 0, the divisor is a factor).
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4. Factorisation of Polynomials

  • SPLITTING THE MIDDLE TERM: For ax^2 + bx + c, find two numbers p and q such that p + q = b and p × q = a × c. Rewrite bx as px + qx and factorise by grouping.
  • USING FACTOR THEOREM for quadratics: Find a zero 'r' by trial, then (x – r) is a factor. Divide to get the other factor.
  • CUBIC FACTORISATION STEPS: (1) Try x = ±1, ±2, ±3, ... (factors of constant term) to find one zero 'a'. (2) Write (x – a) as one factor. (3) Perform grouping or division to find quadratic factor. (4)

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Full Notes

Key Concepts

A polynomial in one variable xEach part of a polynomial separatedThe degree is the highest powerPolynomials are classified by numberA zero of polynomial p(x)

Frequently Asked Questions

What are the important topics in Polynomials for Punjab Board Class 9 Mathematics?
Key topics in Polynomials include Polynomials - Complete Concept Overview, Polynomials Concepts Overview, Decision flowchart to determine if an expression is a polynomial based on whether all exponents are whole numbers. These are the concepts Punjab Board Class 9 examiners draw on most — study them first, then practise related questions.
How to score full marks in Polynomials — Punjab Board Class 9 Mathematics?
Understand the core concepts first, then work through the 45 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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