Question 462870
<pre><font face = "consolas" color = "indigo" size = 4><b>
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
  |<u>    1  -7   4</u> 
    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
   |<u>   -1   9 -20</u> 
     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</pre>