Polynomials — Formula Sheet

Zero of p(x)

A value 'a' such that p(a) = 0

Finding zeros

Solve the equation p(x) = 0

Linear polynomial

exactly one zero at x = -b/a

Division

p(x) = (x - a) × q(x) + p(a)

A polynomial p(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₁x + a₀ where aₙ ≠ 0.

Example

If p(x) = 2x² - 3x + 1, then p(2) = 2(2)² - 3(2) + 1 = 8 - 6 + 1 = 3.

A zero of polynomial p(x) is a value 'a' such that p(a) = 0.