Polynomials Class 9 Maths — Revision Notes
This chapter covers polynomial expressions, their classification, and factorization. Students learn about zeros, factor theorem, and algebraic identities.
TL;DR: This chapter covers polynomial expressions, their classification, and factorization. Students learn about zeros, factor theorem, and algebraic identit…
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This chapter covers polynomial expressions, their classification, and factorization. Students learn about zeros, factor theorem, and algebraic identities.
Polynomial Basics
- Polynomial is algebraic expression with variables and coefficients
- Degree is highest power of variable
- Monomial: single term, Binomial: two terms, Trinomial: three terms
- Leading coefficient is coefficient of highest degree term
Zeros and Factor Theorem
- Zero of polynomial: value of variable making polynomial zero
- Factor theorem: (x - a) is factor if p(a) = 0
- Remainder theorem: remainder when p(x) divided by (x - a) is p(a)
- Polynomial of degree n has at most n zeros
Factorization
- Express polynomial as product of its factors
- Splitting middle term: for ax^2 + bx + c
- Using identities: (a+b)^2, (a-b)^2, a^2-b^2, a^3±b^3
- Grouping method: group terms with common factors
Algebraic Identities
- (a+b)^2 = a^2 + 2ab + b^2
- (a-b)^2 = a^2 - 2ab + b^2
- a^2 - b^2 = (a+b)(a-b)
- (a+b)^3 = a^3 + b^3 + 3ab(a+b)
- a^3 + b^3 = (a+b)(a^2 - ab + b^2)
Key Terms
- Polynomial: Expression with variables and coefficients combined using addition, subtraction, multiplication
- Degree: Highest power of variable in polynomial
- Zero: Value of variable making polynomial equal to zero
Frequently Asked Questions
How do you factorize x^2 + 7x + 12?
Find two numbers with product 12 and sum 7: these are 3 and 4. So x^2 + 7x + 12 = (x+3)(x+4).
What is factor theorem?
If p(a) = 0, then (x-a) is factor of p(x). Conversely, if (x-a) is factor, then p(a) = 0.
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