SOLUTION: 9usquared-9u+2

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Question 129934: 9usquared-9u+2
Answer by jim_thompson5910(35256) About Me  (Show Source):
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Looking at 9u%5E2-9u%2B2 we can see that the first term is 9u%5E2 and the last term is 2 where the coefficients are 9 and 2 respectively.

Now multiply the first coefficient 9 and the last coefficient 2 to get 18. Now what two numbers multiply to 18 and add to the middle coefficient -9? Let's list all of the factors of 18:



Factors of 18:
1,2,3,6,9,18

-1,-2,-3,-6,-9,-18 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 18
1*18
2*9
3*6
(-1)*(-18)
(-2)*(-9)
(-3)*(-6)

note: remember two negative numbers multiplied together make a positive number


Now which of these pairs add to -9? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -9

First NumberSecond NumberSum
1181+18=19
292+9=11
363+6=9
-1-18-1+(-18)=-19
-2-9-2+(-9)=-11
-3-6-3+(-6)=-9



From this list we can see that -3 and -6 add up to -9 and multiply to 18


Now looking at the expression 9u%5E2-9u%2B2, replace -9u with -3u%2B-6u (notice -3u%2B-6u adds up to -9u. So it is equivalent to -9u)

9u%5E2%2Bhighlight%28-3u%2B-6u%29%2B2


Now let's factor 9u%5E2-3u-6u%2B2 by grouping:


%289u%5E2-3u%29%2B%28-6u%2B2%29 Group like terms


3u%283u-1%29-2%283u-1%29 Factor out the GCF of 3u out of the first group. Factor out the GCF of -2 out of the second group


%283u-2%29%283u-1%29 Since we have a common term of 3u-1, we can combine like terms

So 9u%5E2-3u-6u%2B2 factors to %283u-2%29%283u-1%29


So this also means that 9u%5E2-9u%2B2 factors to %283u-2%29%283u-1%29 (since 9u%5E2-9u%2B2 is equivalent to 9u%5E2-3u-6u%2B2)



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Answer:
So 9u%5E2-9u%2B2 factors to %283u-2%29%283u-1%29