SOLUTION: 3n^2+7n+4

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Question 914765: 3n^2+7n+4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Looking at the expression 3n%5E2%2B7n%2B4, we can see that the first coefficient is 3, the second coefficient is 7, and the last term is 4.


Now multiply the first coefficient 3 by the last term 4 to get %283%29%284%29=12.


Now the question is: what two whole numbers multiply to 12 (the previous product) and add to the second coefficient 7?


To find these two numbers, we need to list all of the factors of 12 (the previous product).


Factors of 12:
1,2,3,4,6,12
-1,-2,-3,-4,-6,-12


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


These factors pair up and multiply to 12.
1*12 = 12
2*6 = 12
3*4 = 12
(-1)*(-12) = 12
(-2)*(-6) = 12
(-3)*(-4) = 12

Now let's add up each pair of factors to see if one pair adds to the middle coefficient 7:


First NumberSecond NumberSum
1121+12=13
262+6=8
343+4=7
-1-12-1+(-12)=-13
-2-6-2+(-6)=-8
-3-4-3+(-4)=-7



From the table, we can see that the two numbers 3 and 4 add to 7 (the middle coefficient).


So the two numbers 3 and 4 both multiply to 12 and add to 7


Now replace the middle term 7n with 3n%2B4n. Remember, 3 and 4 add to 7. So this shows us that 3n%2B4n=7n.


3n%5E2%2Bhighlight%283n%2B4n%29%2B4 Replace the second term 7n with 3n%2B4n.


%283n%5E2%2B3n%29%2B%284n%2B4%29 Group the terms into two pairs.


3n%28n%2B1%29%2B%284n%2B4%29 Factor out the GCF 3n from the first group.


3n%28n%2B1%29%2B4%28n%2B1%29 Factor out 4 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.


%283n%2B4%29%28n%2B1%29 Combine like terms. Or factor out the common term n%2B1


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Answer:


So 3n%5E2%2B7n%2B4 factors to %283n%2B4%29%28n%2B1%29.


In other words, 3n%5E2%2B7n%2B4=%283n%2B4%29%28n%2B1%29.


Note: you can check the answer by expanding %283n%2B4%29%28n%2B1%29 to get 3n%5E2%2B7n%2B4 or by graphing the original expression and the answer (the two graphs should be identical).


Let me know if you need more help or if you need me to explain a step in more detail.
Feel free to email me at jim_thompson5910@hotmail.com
or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html

Thanks,

Jim