Question 723112: How do you factor this completely? 6rcubed+15rsquared+8r+20
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! The polynomial  would have a factor of the form 
if  is a zero of the polynomial.
Zeros of that polynomial must be negative because for all  , and 
Any rational zeros will be of the form ,
where  is a factor of the independent term,  , and
 is a factor of the leading coefficient  .
So, could be 1, 2, 3, or 6, and could be 1, 2, 4, 5, 10, or 20.
Since  and  , there must be a zero of  between -2 and -4. Of all the rational possibilities, only  and  are between -2 and -4.
so  is a factor of and dividing by we get  , which cannot be factored further, so
NOTE: If you have gone beyond real numbers and are expected to use complex numbers, you could factor  further.
|
|
|
