SOLUTION: I am factoring trinomials. Doing ok with some, but struggling with ones like one below. Can I change the order of the factored numbers? 3x^2 +7 +2. I factor out 3 to 1

Algebra ->  Equations -> SOLUTION: I am factoring trinomials. Doing ok with some, but struggling with ones like one below. Can I change the order of the factored numbers? 3x^2 +7 +2. I factor out 3 to 1      Log On


   

Question 733115: I am factoring trinomials. Doing ok with some, but struggling with ones like one below. Can I change the order of the factored numbers?
3x^2 +7 +2. I factor out 3 to 1x3. And 2 to 1x2
Then I (1x + 1) (3x +2). But I cannot get it to work or check out properly. Thank you!
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)


Looking at the expression 3x%5E2%2B7x%2B2, we can see that the first coefficient is 3, the second coefficient is 7, and the last term is 2.



Now multiply the first coefficient 3 by the last term 2 to get %283%29%282%29=6.



Now the question is: what two whole numbers multiply to 6 (the previous product) and add to the second coefficient 7?



To find these two numbers, we need to list all of the factors of 6 (the previous product).



Factors of 6:

1,2,3,6

-1,-2,-3,-6



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



These factors pair up and multiply to 6.

1*6 = 6
2*3 = 6
(-1)*(-6) = 6
(-2)*(-3) = 6


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



First NumberSecond NumberSum
161+6=7
232+3=5
-1-6-1+(-6)=-7
-2-3-2+(-3)=-5




From the table, we can see that the two numbers 1 and 6 add to 7 (the middle coefficient).



So the two numbers 1 and 6 both multiply to 6 and add to 7



Now replace the middle term 7x with x%2B6x. Remember, 1 and 6 add to 7. So this shows us that x%2B6x=7x.



3x%5E2%2Bhighlight%28x%2B6x%29%2B2 Replace the second term 7x with x%2B6x.



%283x%5E2%2Bx%29%2B%286x%2B2%29 Group the terms into two pairs.



x%283x%2B1%29%2B%286x%2B2%29 Factor out the GCF x from the first group.



x%283x%2B1%29%2B2%283x%2B1%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.



%28x%2B2%29%283x%2B1%29 Combine like terms. Or factor out the common term 3x%2B1



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Answer:



So 3%2Ax%5E2%2B7%2Ax%2B2 factors to %28x%2B2%29%283x%2B1%29.



In other words, 3%2Ax%5E2%2B7%2Ax%2B2=%28x%2B2%29%283x%2B1%29.



Note: you can check the answer by expanding %28x%2B2%29%283x%2B1%29 to get 3%2Ax%5E2%2B7%2Ax%2B2 or by graphing the original expression and the answer (the two graphs should be identical).