Question 121010: How do I simplify this fraction? How do I factor a four-term polynomial?
Found 2 solutions by nabla, chitra:
Answer by nabla(475)   (Show Source):
You can put this solution on YOUR website! The most straightforward way to simplify such a fraction is to perform long division. Normally, we would factor a 4-term polynomial by grouping, but sometimes it can be more cumbersome in comparison to long division (if that's possible!)
In any case, I will offer you another method that may be new to you. However, it is very powerful, and leads to the correct answer.
Notice that the simplification that we seek is of the form  (We know there will be no remainder as it is implied by the problem that it is able to be simplified). But, we are given the factor of  . So, let's multiply this by our general form:
Now, polynomials are equivalent when their coefficients are equivalent, so we equate the coefficients we just found to the coefficients of the numerator of the problem:
1) 
2)  implies 
3)  implies 
4)  follows
Thus, we can use these coefficients in our "general form" above to see that the simplification of the problem is:
 .
In any case, using long division is the preference when the specific grouping isn't obvious.
Answer by chitra(359) (Show Source):
You can put this solution on YOUR website! We can simplify this fraction, by the long division method.
This is worked as follows:
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x - 1)x^3 + 2x^2 + 3x - 6(x^2 + 3x + 6
x^3 - x^2
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3x^2 + 3x - 6
3x^2 - 3x
------------------
6x - 6
6x - 6
-----------------------
0
the factors are:
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