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Factorisation of Polynomials — Revision Notes

ICSE · Class 10 · Mathematics

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

34 questions26 flashcards12 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

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?
Key topics in Factorisation of Polynomials include Types of polynomials, Division Algorithm for Polynomials, Factor of a polynomial, Value of a polynomial at a number. Study these first, then practise questions on each for the ICSE Class 10 board exam.
How should I revise Factorisation of Polynomials for the ICSE Class 10 board exam?
Learn the core ideas first, then work through the 34 practice questions on Factorisation of 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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