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Factorisation of Polynomials

ICSE · Class 10 · Mathematics

Quick revision notes for Factorisation of Polynomials — ICSE Class 10 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

44 questions22 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

Polynomial Basics and Classification

  • A polynomial p(x) is an algebraic expression of the form p(x) = anx^n + an-1x^(n-1) + ... + a2x^2 + a1x + a0
  • The highest power of x determines the degree of the polynomial
  • Coefficients are the numerical values multiplying each term
2

Division Algorithm for Polynomials

  • When polynomial f(x) is divided by g(x), we get f(x) = g(x) × q(x) + r(x)
  • The remainder r(x) is either zero or has degree less than divisor g(x)
  • If g(x) is linear, remainder is constant; if g(x) is quadratic, remainder is linear or constant
3

Remainder Theorem

  • When polynomial f(x) is divided by (x - a), the remainder is f(a)
  • To find remainder when dividing by (x + a), calculate f(-a)
  • To find remainder when dividing by (ax - b), calculate f(b/a)
4

Factor Theorem

  • (x - a) is a factor of f(x) if and only if f(a) = 0
  • If f(a) = 0, then a is called a zero or root of the polynomial
  • Factor theorem is used to find factors and factorize polynomials completely

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Full Notes

Key Concepts

A polynomial p(x) = aₙxⁿ +For polynomials f(x) ÷ g(x)For polynomial f(x)When polynomial f(x) is divided byFor polynomial f(x)

Frequently Asked Questions

What are the important topics in Factorisation of Polynomials for ICSE Class 10 Mathematics?
Factorisation of Polynomials covers several key topics that are frequently asked in ICSE Class 10 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Factorisation of Polynomials — ICSE Class 10 Mathematics?
Start by understanding all key concepts. Practise previous year questions from this chapter. Revise formulas and definitions regularly. Use flashcards for quick revision 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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