Polynomials — Formula Sheet

Degree 1 → Linear Polynomial (e.g., 2x + 3)

The graph of y = ax + b (linear) is a STRAIGHT LINE that intersects the x-axis at exactly ONE point — (–b/a, 0). So a linear polynomial has exactly 1 zero.

The graph of y = ax² + bx + c (quadratic) is a PARABOLA. It opens upward if a > 0, downward if a < 0.

For a QUADRATIC polynomial p(x) = ax² + bx + c with zeroes α (alpha) and β (beta):

Product of zeroes

αβ = c/a = (constant term) / (coefficient of x²)

Just like in arithmetic (Dividend = Divisor × Quotient + Remainder), polynomials follow the same rule.

DIVISION ALGORITHM

If p(x) is divided by g(x) (g(x) ≠ 0), then p(x) = g(x) × q(x) + r(x), where q(x) is quotient and r(x) is remainder.

The degree of r(x) < degree of g(x), OR r(x) = 0.

Polynomials are classified by their degree

(1) Linear polynomial (degree 1): p(x) = ax + b, where a ≠ 0.

Examples

2x - 3, √3x + 5.

A real number k is called a zero of a polynomial p(x) if p(k) = 0.