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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.

35 questions26 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. Types of polynomials

  • Polynomial classification is done by number of terms and by degree.
  • Monomial means one term, binomial means two terms, and trinomial means three terms.
  • Linear, quadratic, cubic, and constant polynomials are classified by degree.
2

2. Division Algorithm for Polynomials

  • If a polynomial f(x) is divided by a non-zero polynomial g(x), there exist unique polynomials q(x) and r(x) such that f(x)=g(x)q(x)+r(x).
  • Here, f(x) is the dividend, g(x) is the divisor, q(x) is the quotient, and r(x) is the remainder.
  • Either r(x)=0 or deg r(x) < deg g(x).
3

3. Factor of a polynomial

  • A non-zero polynomial g(x) is called a factor of f(x) if and only if there exists a polynomial q(x) such that f(x)=q(x)·g(x).
  • In this case, the remainder is zero.
  • x^2-5x+6 factorises as (x-2)(x-3), so x-2 is a factor of x^2-5x+6.
4

4. Value of a polynomial at a number

  • The value of a polynomial at x=α is obtained by substituting α for x throughout the polynomial.
  • For a polynomial f(x)=a_0x^n+a_1x^{n-1}+...+a_{n-1}x+a_n, the value at x=α is f(α)=a_0α^n+a_1α^{n-1}+...+a_{n-1}α+a_n.
  • Example: for f(x)=x^2+5x+4, the value at x=3 is found by writing f(3)=(3)^2+5(3)+4.

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Full Notes

Key Concepts

Polynomials are classified by numberIf f(x) is divided byA nonThe value of a polynomial atIf a polynomial f(x) is divided

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?
Understand the core concepts first, then work through the 35 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

Sources & Official References

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