SOLUTION: 9y^2+17y-2

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Question 672867: 9y^2+17y-2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Looking at the expression 9y%5E2%2B17y-2, we can see that the first coefficient is 9, the second coefficient is 17, and the last term is -2.


Now multiply the first coefficient 9 by the last term -2 to get %289%29%28-2%29=-18.


Now the question is: what two whole numbers multiply to -18 (the previous product) and add to the second coefficient 17?


To find these two numbers, we need to list all of the factors of -18 (the previous product).


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


Note: list the negative of each factor. This will allow us to find all possible combinations.


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

Now let's add up each pair of factors to see if one pair adds to the middle coefficient 17:


First NumberSecond NumberSum
1-181+(-18)=-17
2-92+(-9)=-7
3-63+(-6)=-3
-118-1+18=17
-29-2+9=7
-36-3+6=3



From the table, we can see that the two numbers -1 and 18 add to 17 (the middle coefficient).


So the two numbers -1 and 18 both multiply to -18 and add to 17


Now replace the middle term 17y with -y%2B18y. Remember, -1 and 18 add to 17. So this shows us that -y%2B18y=17y.


9y%5E2%2Bhighlight%28-y%2B18y%29-2 Replace the second term 17y with -y%2B18y.


%289y%5E2-y%29%2B%2818y-2%29 Group the terms into two pairs.


y%289y-1%29%2B%2818y-2%29 Factor out the GCF y from the first group.


y%289y-1%29%2B2%289y-1%29 Factor out 2 from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.


%28y%2B2%29%289y-1%29 Combine like terms. Or factor out the common term 9y-1


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Answer:


So 9y%5E2%2B17y-2 factors to %28y%2B2%29%289y-1%29.


In other words, 9y%5E2%2B17y-2=%28y%2B2%29%289y-1%29.


Note: you can check the answer by expanding %28y%2B2%29%289y-1%29 to get 9y%5E2%2B17y-2 or by graphing the original expression and the answer (the two graphs should be identical).