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.
Key Topics to Revise
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
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