Polynomials and Factorisation

A polynomial is an algebraic expression

A polynomial is an algebraic expression where variables have only non-negative integer powers. Examples: 3x² + 2x - 1 (polynomial), x^(-1) + 2 (not po

By degree

By degree: Linear (degree 1): ax + b; Quadratic (degree 2): ax² + bx + c; Cubic (degree 3): ax³ + bx² + cx + d. By terms: Monomial (1 term): 5x²; Bino

A zero of polynomial p(x)

A zero of polynomial p(x) is a value 'a' where p(a) = 0. Step-by-step process: 1) Set polynomial equal to zero, 2) Solve for variable, 3) Verify by su

When polynomial p(x) is divided by

When polynomial p(x) is divided by (x - a), remainder = p(a). Step-by-step application: 1) Identify the divisor (x - a), 2) Find 'a' by setting x - a

(x

(x - a) is a factor of p(x) if and only if p(a) = 0. Two-way relationship: If p(a) = 0, then (x - a) is a factor; If (x - a) is a factor, then p(a) =