SOLUTION: 6x^5-11x^4+30x^3 Thank you very much for your help, I need to factor completly.

Question 302560: 6x^5-11x^4+30x^3
Thank you very much for your help, I need to factor completly.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given expression.

Factor out the GCF .

Now let's try to factor the inner expression

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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 :
1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90,180
-1,-2,-3,-4,-5,-6,-9,-10,-12,-15,-18,-20,-30,-36,-45,-60,-90,-180

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

These factors pair up and multiply to .
1*180 = 180
2*90 = 180
3*60 = 180
4*45 = 180
5*36 = 180
6*30 = 180
9*20 = 180
10*18 = 180
12*15 = 180
(-1)*(-180) = 180
(-2)*(-90) = 180
(-3)*(-60) = 180
(-4)*(-45) = 180
(-5)*(-36) = 180
(-6)*(-30) = 180
(-9)*(-20) = 180
(-10)*(-18) = 180
(-12)*(-15) = 180

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	180	1+180=181
2	90	2+90=92
3	60	3+60=63
4	45	4+45=49
5	36	5+36=41
6	30	6+30=36
9	20	9+20=29
10	18	10+18=28
12	15	12+15=27
-1	-180	-1+(-180)=-181
-2	-90	-2+(-90)=-92
-3	-60	-3+(-60)=-63
-4	-45	-4+(-45)=-49
-5	-36	-5+(-36)=-41
-6	-30	-6+(-30)=-36
-9	-20	-9+(-20)=-29
-10	-18	-10+(-18)=-28
-12	-15	-12+(-15)=-27

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

===============================================================

Answer:

So simply factors to

In other words, .

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