You can
put this solution on YOUR website! Can you factor (t³-8)?
Yes, it's the difference of two cubes, t³ - 2³
It can be divided by t - 2.
We first write t³ - 8 as t³ + 0t² + 0t - 8
t² + 2t + 4
t - 2)t³ + 0t² + 0t - 8
t³ - 2t²
2t² + 0t
2t² - 4t
4t - 8
4t - 8
0
That means t³ - 2³ factors as (t - 2)(t² + 2t + 4)
To save having to do long division every time, memorize
this:
A³ + B³ factors as (A + B)(A - AB + B²)
and
A³ - B³ factors as (A - B)(A + AB + B²)
Edwin
