Hi everyone, I have a math problem and I'm looking for the fastest way to solve it. I need to factor polynomials of degree 1, 2, 3, or 4 into their constituent factors (whenever possible). When I use a handheld calculator to find the roots of an equation, sometimes it provides fewer roots than the degree of the polynomial (for example, a cubic equation might only show 2 roots, or a quartic might show 2 or 3).

When writing the factors back out, I struggle to quickly determine where to place the exponents (i.e., which roots are simple and which are repeated). Currently, I have to test each case manually, which is extremely time-consuming. Does anyone have any ideas or tips for solving this more efficiently? Thanks!