x³ - 8x² + 11x + 20
The possible rational zeros are ± the factors of 20:
±1, ±2, ±4, ±5, ±10, ±20
We will start out trying 1
1 | 1 -8 11 20
| 1 -7 4
1 -7 4 24
No, 1 is not a zero because we got a remainder
of 24, not 0. So we will try -1
-1 | 1 -8 11 20
| -1 9 -20
1 -9 20 0
This time we got a zero remainder, so we have
factored
x³ - 8x² + 11x + 20
as
(x + 1)(x² - 9x + 20)
The expression in the second parentheses will
factor again
(x + 1)(x - 4)(x - 5)
That's it.
Edwin
