SOLUTION: Hi, I am trying to figure out this factoring of trinomials. I didn't see where there were any questions on this particular subject, but thought you could help. 14b^3-33b^2+

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Question 148737: Hi, I am trying to figure out this factoring of trinomials. I didn't see where there were any questions on this particular subject, but thought you could help.
14b^3-33b^2+18b
Thank you for any help you are able to give.
Found 2 solutions by oscargut, jim_thompson5910:
Answer by oscargut(2103)   (Show Source): You can put this solution on YOUR website!
14b^3-33b^2+18b=b(14b^2-33b+18)

14b^2-33b+18=0 then
=
=

then b=42/28 or x=24/28
then b=3/2 or x=6/7
then
14b^2-33b+18=14(b-3/2)(b-6/7)
Answer:14b^3-33b^2+18b = 14b(b-3/2)(b-6/7)


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 focus on 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 :
1,2,3,4,6,7,9,12,14,18,21,28,36,42,63,84,126,252
-1,-2,-3,-4,-6,-7,-9,-12,-14,-18,-21,-28,-36,-42,-63,-84,-126,-252


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


These factors pair up and multiply to . For instance, , , etc.


Since is positive, this means that either
a) both factors are positive, or...
b) both factors are negative.


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


First NumberSecond NumberSum
12521+252=253
21262+126=128
3843+84=87
4634+63=67
6426+42=48
7367+36=43
9289+28=37
122112+21=33
141814+18=32
-1-252-1+(-252)=-253
-2-126-2+(-126)=-128
-3-84-3+(-84)=-87
-4-63-4+(-63)=-67
-6-42-6+(-42)=-48
-7-36-7+(-36)=-43
-9-28-9+(-28)=-37
-12-21-12+(-21)=-33
-14-18-14+(-18)=-32



From the table, we can see that the two numbers and add to (the middle coefficient).


So the two numbers and both multiply to and add to


Now replace the middle term with . Remember, and add to . So this shows us that .


Replace the second term with .


Group the terms into two pairs.


Factor out the GCF from the first group.


Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.


Combine like terms. Or factor out the common term


So factors to .



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


Now go back to the second step.



Replace with .


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


Answer:



So factors to .

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