SOLUTION: what is the factored form of 4k^3-13k^2-12k

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Question 387109: what is the factored form of 4k^3-13k^2-12k
Found 2 solutions by jim_thompson5910, tara0066:
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 :
1,2,3,4,6,8,12,16,24,48
-1,-2,-3,-4,-6,-8,-12,-16,-24,-48


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


These factors pair up and multiply to .
1*(-48) = -48
2*(-24) = -48
3*(-16) = -48
4*(-12) = -48
6*(-8) = -48
(-1)*(48) = -48
(-2)*(24) = -48
(-3)*(16) = -48
(-4)*(12) = -48
(-6)*(8) = -48

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


First NumberSecond NumberSum
1-481+(-48)=-47
2-242+(-24)=-22
3-163+(-16)=-13
4-124+(-12)=-8
6-86+(-8)=-2
-148-1+48=47
-224-2+24=22
-316-3+16=13
-412-4+12=8
-68-6+8=2



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 then factors further to


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


Answer:


So completely factors to .


In other words, .


Note: you can check the answer by expanding to get or by graphing the original expression and the answer (the two graphs should be identical).


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim
Answer by tara0066(31)   (Show Source): You can put this solution on YOUR website!
k(4k^2-13k-12) Pull out what they have in common, in this case a k
Multiply your first value (4) and last value (-12). Find a number that multiplies to get -48 and their sum comes to -13 (which is your middle term).
3(-16) works for both situations.
k[4k^2-16k+3k-12] Replaced middle term with the values you found. Order doesn't matter.
k[4k(k-4)+3(k-4)] Split the 4 terms into two sets and pull out what the pairs have in common. Your two parenthesis inside should always match if you did this right.
k(k-4)(4k+3) Write the repeated set once and the other set comes from the values that you factored out. Don't forget the k from the beginning that was pulled out. It is still out there.
Hard to follow this one. A little complicated. Hope you could stay with me. lol. Good luck.
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