Polynomials — Formula Sheet

The highest power of x in p(x) is called the degree of the polynomial p(x).

Zero of a polynomial: p(k) = 0

Zero of linear polynomial ax + b: k = -b/a

Linear graph: y = ax + b

Quadratic graph: y = ax^2 + bx + c

Maximum zeroes of degree n polynomial: at most n

For ax^2 + bx + c, α + β = -b/a

For ax^2 + bx + c, αβ = c/a

Quadratic from sum and product: k(x^2 - (sum)x + product)

For ax^3 + bx^2 + cx + d, α + β + γ = -b/a

For ax^3 + bx^2 + cx + d, αβ + βγ + γα = c/a

For ax^3 + bx^2 + cx + d, αβγ = -d/a

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

For a quadratic polynomial ax^2 + bx + c, if the zeroes are α and β, then α + β = -b/a and αβ = c/a.