SOLUTION: Can you help me solve this question. I cannot factor to get the answer 18x^4 * 6x^2+19x+3 x^3+3x^2-9x-27 18x^2+3x

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Can you help me solve this question. I cannot factor to get the answer 18x^4 * 6x^2+19x+3 x^3+3x^2-9x-27 18x^2+3x       Log On


   

Question 752756: Can you help me solve this question. I cannot factor to get the answer
18x^4 * 6x^2+19x+3
x^3+3x^2-9x-27 18x^2+3x

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
18x^4 * 6x^2+19x+3
x^3+3x^2-9x-27 18x^2+3x
%2818x%5E4%29%2F%28x%5E3%2B3x%5E2-9x-27%29%22%22%2A%22%22%286x%5E2%2B19x%2B3%29%2F%2818x%5E2%2B3x%29

You must learn to factor in order to do this kind of problem.

%2818x%5E4%29%2F%28x%5E3%2B3x%5E2-9x-27%29%22%22%2A%22%22%286x%5E2%2B19%2B3%29%2F%2818x%5E2%2B3x%29

You must learn to factor the lower left denominator by grouping:

x³+3x²-9x-27
x²(x+3)-9(x+3)
(x+3)(x²-9)
(x+3)(x-3)(x+3)

You must learn to factor the upper right numerator either by the
AC method or by the guess and check method:

6x²+19x+3
(6x+1)(x+3)

You must learn to factor the lower right denominator by taking out
a common factor:

18x²+3x
3x(6x+1)


%2818x%5E4%29%2F%28%28x-3%29%28x-3%29%28x%2B3%29%29%22%22%2A%22%22%28%286x%2B1%29%28x%2B3%29%29%2F%283x%286x%2B1%29%29

Indicate the multiplication of numerators and denominators
making just one fraction:
        
%2818x%5E4%286x%2B1%29%28x%2B3%29%29%2F%28%28x%2B3%29%28x-3%29%28x%2B3%293x%286x%2B1%29%29

Now you can cancel what will cancel.  You can do it all in one step,
but I'll just cancel one thing at a time:

Cancel the 3 on the bottom into the 18 on top, getting 6 on top:



%286x%5E4%286x%2B1%29%28x%2B3%29%29%2F%28%28x%2B3%29%28x-3%29%28x%2B3%29x%286x%2B1%29%29

Cancel the x on the bottom into the x4 on top, getting x3
on top:

    ³


%286x%5E3%286x%2B1%29%28x%2B3%29%29%2F%28%28x%2B3%29%28x-3%29%28x%2B3%29%286x%2B1%29%29

Cancel the (6x+1)'s:





%286x%5E3%28x%2B3%29%29%2F%28%28x%2B3%29%28x-3%29%28x%2B3%29%29

Cancel the (x+3)'s

%286x%5E3%28cross%28x%2B3%29%29%29%2F%28%28x%2B3%29%28x-3%29%28cross%28x%2B3%29%29%29

%286x%5E3%29%2F%28%28x%2B3%29%28x-3%29%29

You can leave it like that, since nothing else will cancel.
As I said above you can do all that canceling in one step.

Edwin