Factorisation of Polynomials
ICSE · Class 10 · Mathematics
Complete topic list for Factorisation of Polynomials in ICSE Class 10 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.
Topics in Factorisation of Polynomials
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
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
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)
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
Key Concepts
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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.
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