SOLUTION: How do you factor this completely? 6rcubed+15rsquared+8r+20

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.
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