Question 183103
<pre><font size = 4 color = "indigo"><b>
f(x) = x³ + 2x² - 51x + 108 

Divide x³ + 2x² - 51x + 108 by x + 9, 
either by long division:


     <u>        x² -  7x +  12</u> 
x + 9)x³ +  2x² - 51x + 108 
      <u>x³ +  9x²</u>  
           -7x² - 51x  
           <u>-7x² - 63x</u>
                  12x + 108 
                  <u>12x + 108</u>
                          0
                
or by, what amounts to the same thing,
synthetic division, if you've studied
that:

 -9|1   2  -51  108
   |<u>   -9   63 -108</u>  
    1  -7   12    0

Either way, thus far you have factored the
original cubic polynomial f(x) as:

(x + 9)(x² -  7x +  12)

Now we can factor the quadratic
polynomial in the second parentheses
as (x - 3)(x - 4) and the complete
factorization of f(x) into prime
linear factors is:

(x + 9)(x - 3)(x - 4)

So the other two prime linear factors of
f(x) are (x - 3) and (x - 4).

Edwin</pre>