SOLUTION: Factor completely and show the check by re-multiplication. If the polynominal is not factorable, write "prime". 1.) 12x^3-20x^2-8x 2.) 42x^2-23x-5 Thank you.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Factor completely and show the check by re-multiplication. If the polynominal is not factorable, write "prime". 1.) 12x^3-20x^2-8x 2.) 42x^2-23x-5 Thank you.      Log On


   

Question 1067762: Factor completely and show the check by re-multiplication. If the polynominal is not factorable, write "prime".
1.) 12x^3-20x^2-8x
2.) 42x^2-23x-5
Thank you.
Found 2 solutions by Boreal, Edwin McCravy:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
12x^3-20x^2-8x
4x can be divided out
4x(3x^2-5x-2)=4x(3x+1)(x-2)
4x*(3x^2-6x+x-2)=12x^3-24x^2+4x^2-8x
-------------------
42x^2-23x-5
divide 42 from first and multiply last term by 42
x^2-23x-210, which factors into (x+7)(x-30)
divide those by 42 and reduce completely
(x+7/42)(x-30/42)=(x+(1/6))(x-(5/7))
move the denominator of the fraction in front of the x
(6x+1)(7x-5)
42x^2-30x+7x-5

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
12x%5E3-20x%5E2-8x

Factor out 4x

4x%283x%5E2-5x-2%29

Multiply 3 times -2, get -6
Think of two integers that when multiplied give -6,
yet when combined give -5.  If you think hard enough,
you'll come up with -6 and +1, because when multiplied
they give -6 and when combined they give -5.  So write
-5x as -6x+1x

4x%283x%5E2-6x%2B1x-2%29

Factor 3x out of the first two terms inside the parentheses:

4x%283x%28x-2%29%5E%22%22%2B1x-2%29

Factor +1 out of the last two terms inside the parentheses: 

4x%283x%28x-2%29%5E%22%22%2B1%28x-2%29%5E%22%22%29

Factor (x-2) out of both terms in the big parentheses:

4x%28%28x-2%29%283x%2B1%29%5E%22%22%29

Drop the big parentheses:

4x%28x-2%29%283x%2B1%29

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

42x%5E2-23x-5

Try breaking up 42x² as 6x time 7x

%28matrix%281%2C3%2C6x%2C%22%22%2C%22%22%29%29%28matrix%281%2C3%2C7x%2C%22%22%2C%22%22%29%29

Ignoring the sign of -5, try breaking up 5 as 5 times 1 or as 1 times 5

%28matrix%281%2C3%2C6x%2C%22%22%2C5%29%29%28matrix%281%2C3%2C7x%2C%22%22%2C1%29%29 or %28matrix%281%2C3%2C6x%2C%22%22%2C1%29%29%28matrix%281%2C3%2C7x%2C%22%22%2C5%29%29

There is no way to put signs in to make FOIL word, but
there is for the second one.



Now you check by multiplying them out using FOIL or distributing.

Edwin