SOLUTION: 6x^3 - 6x = 16x^2 I need a step by step explanation on how you get to the answers, once I get to x(6x^2 -16x-6) I get lost on how to break the next step down. Please help.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 6x^3 - 6x = 16x^2 I need a step by step explanation on how you get to the answers, once I get to x(6x^2 -16x-6) I get lost on how to break the next step down. Please help.       Log On


   

Question 838365: 6x^3 - 6x = 16x^2
I need a step by step explanation on how you get to the answers, once I get to
x(6x^2 -16x-6) I get lost on how to break the next step down. Please help.
Thanks,
Nancy
Found 2 solutions by richwmiller, ewatrrr:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
x=0
x=-1/3
x=3
Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)


6%2Ax%5E2-16%2Ax-6 Start with the given expression.



2%283x%5E2-8x-3%29 Factor out the GCF 2.



Now let's try to factor the inner expression 3x%5E2-8x-3



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Looking at the expression 3x%5E2-8x-3, we can see that the first coefficient is 3, the second coefficient is -8, and the last term is -3.



Now multiply the first coefficient 3 by the last term -3 to get %283%29%28-3%29=-9.



Now the question is: what two whole numbers multiply to -9 (the previous product) and add to the second coefficient -8?



To find these two numbers, we need to list all of the factors of -9 (the previous product).



Factors of -9:

1,3,9

-1,-3,-9



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



These factors pair up and multiply to -9.

1*(-9) = -9
3*(-3) = -9
(-1)*(9) = -9
(-3)*(3) = -9


Now let's add up each pair of factors to see if one pair adds to the middle coefficient -8:



First NumberSecond NumberSum
1-91+(-9)=-8
3-33+(-3)=0
-19-1+9=8
-33-3+3=0




From the table, we can see that the two numbers 1 and -9 add to -8 (the middle coefficient).



So the two numbers 1 and -9 both multiply to -9 and add to -8



Now replace the middle term -8x with x-9x. Remember, 1 and -9 add to -8. So this shows us that x-9x=-8x.



3x%5E2%2Bhighlight%28x-9x%29-3 Replace the second term -8x with x-9x.



%283x%5E2%2Bx%29%2B%28-9x-3%29 Group the terms into two pairs.



x%283x%2B1%29%2B%28-9x-3%29 Factor out the GCF x from the first group.



x%283x%2B1%29-3%283x%2B1%29 Factor out 3 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.



%28x-3%29%283x%2B1%29 Combine like terms. Or factor out the common term 3x%2B1



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So 2%283x%5E2-8x-3%29 then factors further to 2%28x-3%29%283x%2B1%29



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Answer:



So 6%2Ax%5E2-16%2Ax-6 completely factors to 2%28x-3%29%283x%2B1%29.



In other words, 6%2Ax%5E2-16%2Ax-6=2%28x-3%29%283x%2B1%29.



Note: you can check the answer by expanding 2%28x-3%29%283x%2B1%29 to get 6%2Ax%5E2-16%2Ax-6 or by graphing the original expression and the answer (the two graphs should be identical).

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

x(6x^2 -16x-6)= 0   |Need to factor 6x^2 -16x-6

x(3x+1)(2x-6) = 0

Use FOIL to check the factoring

F	First terms  6x^2

O	Outside terms -18x

I	Inside terms    2x

L	Last terms    -6