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Polynomials — Revision Notes

Punjab Board · Class 9 · Mathematics

Polynomials revision notes for Punjab Board Class 9 Mathematics: 4 topics in quick points. Part of the Punjab Board Class 9 Mathematics syllabus.

45 questions32 flashcards5 formulas & key relations5 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

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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 in One Variable – Basic Concepts, Zeroes of a Polynomial, Remainder Theorem and Factor Theorem, Factorisation of Polynomials. Study these first, then practise questions on each for Class 9 exams.
How should I revise Polynomials for Class 9 exams?
Learn the core ideas first, then work through the 45 practice questions on Polynomials. Revise 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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All Punjab Board Class 9 Mathematics Revision Notes

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