Cubic polynomials

A cubic polynomial is a polynomial of degree 3, written as $P(x) = ax^3 + bx^2 + cx + d$ with $a \neq 0$. Cubic polynomials can have up to three real roots and always have three complex roots (counting multiplicity).

Important properties

• The graph of a cubic polynomial is a smooth curve with at most two turning points.

• A cubic polynomial always has at least one real root.

• The sum of the roots is $-b/a$, the product is $-d/a$.

• Cubic polynomials can be factored if roots are known.