SOLUTION: 2. Compute and simplify the diffence quotient g(x)=6x^2+10x-1

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Question 265973: 2. Compute and simplify the diffence quotient
g(x)=6x^2+10x-1

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
2. Compute and simplify the difference quotient
g(x)=6x^2+10x-1

difference_quotient+=+%28%22g%28x%2Bh%29%22-%22g%28x%29%22%29%2Fh

To the side let's calculate and simplify the most 
complicated part, the first term on top, which is 
g%28x%2Bh%29:

%22g%28x%29%22=6x%5E2%2B10x-1
%22g%28x%2Bh%29%22=6%28x%2Bh%29%5E2%2B10%28x%2Bh%29-1
%22g%28x%2Bh%29%22=6%28x%5E2%2B2xh%2Bh%5E2%29%2B10x%2B10h-1
%22g%28x%2Bh%29%22=6x%5E2%2B12xh%2B6h%5E2%2B10x%2B10h-1


Now we can substitute that into the right side of

difference_quotient+=+%28%22g%28x%2Bh%29%22-%22g%28x%29%22%29%2Fh

for the %22g%28x%2Bh%29%22

difference_quotient+=+%286x%5E2%2B12xh%2B6h%5E2%2B10x%2B10h-1-%22g%28x%29%22%29%2Fh

And for %22g%28x%29%22 we just substitute 
%286x%5E2%2B10x-1%29 (enclosed in parentheses)

difference_quotient+=+%286x%5E2%2B12xh%2B6h%5E2%2B10x%2B10h-1-%286x%5E2%2B10x-1%29%29%2Fh 

Remove the parentheses on top

difference_quotient+=+%286x%5E2%2B12xh%2B6h%5E2%2B10x%2B10h-1-6x%5E2-10x%2B1%29%2Fh

Now every term on top will cancel except those which contain factor h:



difference_quotient+=+%2812xh%2B6h%5E2%2B10h%29%2Fh

Factor h out of the top:

difference_quotient+=+%28h%2812x%2B6h%2B10%29%29%2Fh

Cancel the h's:

difference_quotient+=+%28cross%28h%29%2812x%2B6h%2B10%29%29%2Fcross%28h%29

difference_quotient+=+12x%2B6h%2B10%29

Edwin