Question

How do you factor `z^3+2z^2+z+2`?

Answer 1

Look for two pairs of terms which share a common factor between the pairs.
In this case
the pair `color(red)(z^3+2z)` and
the pair `color(blue)(z+2)`
share a common factor: `color(green)(z+2)`

`color(red)(z^3+2z^2) + color(blue)(z+2)`

`= (z^2)color(green)((z+2))+(1)color(green)((z+2))`

`= (z^2+1)color(green)((z+2))`