Question

How do I factor completely, e.g. 2x^3+7x^2+6x+21

Answer 1

\[ (7+2 x) \left(3+x^2\right) \]

Answer 2

how?

Answer 3

This is done easiest through the grouping method.
\[2x^3+7x^2+6x+21=(2x^3+6x)+(7x^2+21)\]\[=2x(x^2+3)+7(x^2+3)\]\[=(x^2+3)(2x+7)\]
All we are doing is taking out common factors. :)