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Polynomials — Revision Notes

Punjab Board · Class 10 · Mathematics

Polynomials revision notes for Punjab Board Class 10 Mathematics: 4 topics in quick points. Part of the Punjab Board Class 10 Mathematics syllabus.

45 questions25 flashcards11 formulas & key relations5 concepts

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Key Topics to Revise

1

Types of Polynomials and Basic Definitions

  • A polynomial p(x) in one variable x is an expression of the form aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₁x + a₀, where all coefficients are real numbers and n is a non-negative integer.
  • The highest power of x in a polynomial is called its DEGREE.
  • Degree 1 → Linear Polynomial (e.g., 2x + 3)
2

Geometrical Meaning of Zeroes of a Polynomial

  • The graph of y = ax + b (linear) is a STRAIGHT LINE that intersects the x-axis at exactly ONE point — (–b/a, 0). So a linear polynomial has exactly 1 zero.
  • The graph of y = ax² + bx + c (quadratic) is a PARABOLA. It opens upward if a > 0, downward if a < 0.
  • KEY RULE: The zeroes of any polynomial p(x) are the x-COORDINATES of points where the graph y = p(x) intersects (crosses or touches) the x-axis.
3

Relationship Between Zeroes and Coefficients

  • For a QUADRATIC polynomial p(x) = ax² + bx + c with zeroes α (alpha) and β (beta):
  • Sum of zeroes: α + β = –b/a = –(coefficient of x) / (coefficient of x²)
  • Product of zeroes: αβ = c/a = (constant term) / (coefficient of x²)
4

Division Algorithm for Polynomials

  • Just like in arithmetic (Dividend = Divisor × Quotient + Remainder), polynomials follow the same rule.
  • DIVISION ALGORITHM: If p(x) is divided by g(x) (g(x) ≠ 0), then p(x) = g(x) × q(x) + r(x), where q(x) is quotient and r(x) is remainder.
  • The degree of r(x) < degree of g(x), OR r(x) = 0.

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Full Notes

Key Concepts

A polynomial in one variablePolynomials are classified by their degreeIf p(x) is a polynomialA real number k is calledFor a linear polynomial p(x) =

Frequently Asked Questions

What are the important topics in Polynomials for Punjab Board Class 10 Mathematics?
Key topics in Polynomials include Types of Polynomials and Basic Definitions, Geometrical Meaning of Zeroes of a Polynomial, Relationship Between Zeroes and Coefficients, Division Algorithm for Polynomials. Study these first, then practise questions on each for the Punjab Board Class 10 board exam.
How should I revise Polynomials for the Punjab Board Class 10 board exam?
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 10 Mathematics Revision Notes

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