Precalculus · Problem 3.3.17

The key is to notice that this cubic has a hidden structure: try factoring by grouping pairs of terms. Once you uncover a common factor, you'll reduce the problem to a quadratic, which you can then solve using standard methods. Multiplicity tells you how many times each zero appears as a factor—if $(x - a)^2$ divides $f(x)$, then $x = a$ has multiplicity 2.

The key is to notice that this cubic has a hidden structure: try factoring by grouping pairs of terms. Once you uncover a common factor, you'll reduce the problem to a quadratic, which you can then solve using standard methods. Multiplicity tells you how many times each zero appears as a factor—if $(x - a)^2$ divides $f(x)$, then $x = a$ has multiplicity 2.