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Polynomials

Punjab Board · Class 10 · Mathematics

Quick revision notes for Polynomials — Punjab Board Class 10 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

45 questions25 flashcards5 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 Polynomials – Complete Chapter Overview, Polynomials - Comprehensive Concept Overview, Polynomials – Complete Chapter Overview. These are the concepts Punjab Board Class 10 examiners draw on most — study them first, then practise related questions.
How to score full marks in Polynomials — Punjab Board Class 10 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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All 5 chapters — Punjab Board Class 10 Mathematics Revision Notes

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