Factor:
x³ - 8x² + 11x + 20
If there are any rational zeros they must be ± divisors
of 20, which are ±1, ±2, ±4, ±5, ±10, ±20.
We try the easiest, 1, using synthetic division:
1| 1 -8 11 20
| 1 -7 4
1 -7 4 24
No that gives remainder 24, not 0
We try the next easiest, -1:
-1| 1 -8 11 20
| -1 9 -20
1 -9 20 0
That gives remainder 0, so (x + 1) is a factor of
the polynomial. Therefore
(x + 1)(x² - 9x + 20)
is a partial factorization, but not a complete
factorization, because the binomial in the second
parentheses can be factored, and the final
factorization is:
(x + 1)(x - 5)(x - 4)
Edwin
