SOLUTION: Please help me with this question 3n(squared) + 2n - 1. Thank You

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Question 190939: Please help me with this question 3n(squared) + 2n - 1. Thank You
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming you want to factor?


Looking at the expression 3n%5E2%2B2n-1, we can see that the first coefficient is 3, the second coefficient is 2, and the last term is -1.


Now multiply the first coefficient 3 by the last term -1 to get %283%29%28-1%29=-3.


Now the question is: what two whole numbers multiply to -3 (the previous product) and add to the second coefficient 2?


To find these two numbers, we need to list all of the factors of -3 (the previous product).


Factors of -3:
1,3
-1,-3


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


These factors pair up and multiply to -3.
1*(-3)
(-1)*(3)

Now let's add up each pair of factors to see if one pair adds to the middle coefficient 2:


First NumberSecond NumberSum
1-31+(-3)=-2
-13-1+3=2



From the table, we can see that the two numbers -1 and 3 add to 2 (the middle coefficient).


So the two numbers -1 and 3 both multiply to -3 and add to 2


Now replace the middle term 2n with -n%2B3n. Remember, -1 and 3 add to 2. So this shows us that -n%2B3n=2n.


3n%5E2%2Bhighlight%28-n%2B3n%29-1 Replace the second term 2n with -n%2B3n.


%283n%5E2-n%29%2B%283n-1%29 Group the terms into two pairs.


n%283n-1%29%2B%283n-1%29 Factor out the GCF n from the first group.


n%283n-1%29%2B1%283n-1%29 Factor out 1 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.


%28n%2B1%29%283n-1%29 Combine like terms. Or factor out the common term 3n-1

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Answer:


So 3n%5E2%2B2n-1 factors to %28n%2B1%29%283n-1%29.


Note: you can check the answer by FOILing %28n%2B1%29%283n-1%29 to get 3n%5E2%2B2n-1 or by graphing the original expression and the answer (the two graphs should be identical).