Question 129934
Do you want to factor?





Looking at {{{9u^2-9u+2}}} we can see that the first term is {{{9u^2}}} 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


<table border="1"><th>First Number</th><th>Second Number</th><th>Sum</th><tr><td align="center">1</td><td align="center">18</td><td>1+18=19</td></tr><tr><td align="center">2</td><td align="center">9</td><td>2+9=11</td></tr><tr><td align="center">3</td><td align="center">6</td><td>3+6=9</td></tr><tr><td align="center">-1</td><td align="center">-18</td><td>-1+(-18)=-19</td></tr><tr><td align="center">-2</td><td align="center">-9</td><td>-2+(-9)=-11</td></tr><tr><td align="center">-3</td><td align="center">-6</td><td>-3+(-6)=-9</td></tr></table>



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



Now looking at the expression {{{9u^2-9u+2}}}, replace {{{-9u}}} with {{{-3u+-6u}}} (notice {{{-3u+-6u}}} adds up to {{{-9u}}}. So it is equivalent to {{{-9u}}})


{{{9u^2+highlight(-3u+-6u)+2}}}



Now let's factor {{{9u^2-3u-6u+2}}} by grouping:



{{{(9u^2-3u)+(-6u+2)}}} Group like terms



{{{3u(3u-1)-2(3u-1)}}} Factor out the GCF of {{{3u}}} out of the first group. Factor out the GCF of {{{-2}}} out of the second group



{{{(3u-2)(3u-1)}}} Since we have a common term of {{{3u-1}}}, we can combine like terms


So {{{9u^2-3u-6u+2}}} factors to {{{(3u-2)(3u-1)}}}



So this also means that {{{9u^2-9u+2}}} factors to {{{(3u-2)(3u-1)}}} (since {{{9u^2-9u+2}}} is equivalent to {{{9u^2-3u-6u+2}}})




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     Answer:

So {{{9u^2-9u+2}}} factors to {{{(3u-2)(3u-1)}}}