SOLUTION: Factor. Remember to use the largest common factor and to check by multiplying. Factor out a negative factor if the first coefficient is negative. -10t^5+15t^4+9t^3

Question 616008: Factor. Remember to use the largest common factor and to check by multiplying. Factor out a negative factor if the first coefficient is negative.
-10t^5+15t^4+9t^3

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

---------------------------------------------------------------

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 :
1,2,3,5,6,9,10,15,18,30,45,90
-1,-2,-3,-5,-6,-9,-10,-15,-18,-30,-45,-90

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

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

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	-90	1+(-90)=-89
2	-45	2+(-45)=-43
3	-30	3+(-30)=-27
5	-18	5+(-18)=-13
6	-15	6+(-15)=-9
9	-10	9+(-10)=-1
-1	90	-1+90=89
-2	45	-2+45=43
-3	30	-3+30=27
-5	18	-5+18=13
-6	15	-6+15=9
-9	10	-9+10=1

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, .

RELATED QUESTIONS
factor. remember to use the largest common factor and to check by multiplying. factor out (answered by Alan3354)

Factor. Remember to use the largest common factor and to check by multiplying. Factor out (answered by stanbon)

Factor. Remember to use the largest common factor and to check by multiplying. factor and (answered by Alan3354)

Factor completely. Remember to look first for a common factor and to check by multiplying (answered by ewatrrr)

Factor completely. Remember to look first for a common factor and to check by... (answered by lynnlo)

Factor completely. Remember to look first for a common factor and to check by... (answered by ankor@dixie-net.com)

Factor completely. Remember to look first for a common factor and to check by... (answered by nerdybill)

Factor completely. Remember to look first for a common factor and to check by... (answered by richwmiller)