Factoring a cubic is the process of expressing a cubic polynomial as a product of three linear factors. A cubic polynomial is a polynomial of degree three, which means that it is a polynomial of the form ax + bx + cx + d, where a, b, c, and d are constants and a 0. Factoring a cubic is important because it allows us to solve cubic equations, which are equations of the form ax + bx + cx + d = 0. Solving a cubic equation by factoring involves finding the three linear factors of the cubic polynomial and then setting each factor equal to zero.
There are a few different methods for factoring a cubic. One common method is to use the Rational Root Theorem, which states that if a polynomial has a rational root p/q (where p and q are integers and q 0), then p is a factor of the constant term and q is a factor of the leading coefficient. Another method for factoring a cubic is to use Vieta’s Formulas, which relate the coefficients of a polynomial to the sum, product, and other relationships between its roots. Once the linear factors of a cubic polynomial have been found, the polynomial can be factored as a product of those factors.
