Question

How can the techniques of factoring be extended to work with higher-degree polynomials?

Answer 1

Explanation:

Any techniques that you're familiar with can be applied to polynomials of any degree. These might include ...

• use of the rational root theorem
• use of Descartes' rule of signs
• use of any algorithms you're aware of for finding bounds on roots
• graphing
• factoring by grouping
• use of "special forms" (for example, difference of squares, sum and difference of cubes, square of binomials, expansion of n-th powers of binomials)
• guess and check
• making use of turning points

Each root you find can be factored out to reduce the degree of the remaining polynomial factor(s).