SOLUTION: How to solve this, 6x^3-6x^2-x+1 by factoring through grouping.

Question 392345: How to solve this, 6x^3-6x^2-x+1 by factoring through grouping.
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!

let see if

Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)

Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .

Now multiply the first coefficient by the last term to get .

Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?

To find these two numbers, we need to list all of the factors of (the previous product).

Factors of :

1,2,3,6

-1,-2,-3,-6

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to .

1*(-6) = -6
2*(-3) = -6
(-1)*(6) = -6
(-2)*(3) = -6

Now let's add up each pair of factors to see if one pair adds to the middle coefficient :

First Number	Second Number	Sum
1	-6	1+(-6)=-5
2	-3	2+(-3)=-1
-1	6	-1+6=5
-2	3	-2+3=1

From the table, we can see that there are no pairs of numbers which add to . So cannot be factored.

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Answer:

So doesn't factor at all (over the rational numbers).

So is prime.

since cannot be factored, this is your answer:
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