SOLUTION: how to factor 3x^2-13x+4

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Question 816885: how to factor
3x^2-13x+4
Found 2 solutions by richwmiller, ewatrrr:
Answer by richwmiller(17219) 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%5E2-13x%2B4, we can see that the first coefficient is 3, the second coefficient is -13, 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 -13?



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 -13:



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 -1 and -12 add to -13 (the middle coefficient).



So the two numbers -1 and -12 both multiply to 12 and add to -13



Now replace the middle term -13x with -x-12x. Remember, -1 and -12 add to -13. So this shows us that -x-12x=-13x.



3x%5E2%2Bhighlight%28-x-12x%29%2B4 Replace the second term -13x with -x-12x.



%283x%5E2-x%29%2B%28-12x%2B4%29 Group the terms into two pairs.



x%283x-1%29%2B%28-12x%2B4%29 Factor out the GCF x from the first group.



x%283x-1%29-4%283x-1%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.



%28x-4%29%283x-1%29 Combine like terms. Or factor out the common term 3x-1



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Answer:



So 3%2Ax%5E2-13%2Ax%2B4 factors to %28x-4%29%283x-1%29.



In other words, 3%2Ax%5E2-13%2Ax%2B4=%28x-4%29%283x-1%29.



Note: you can check the answer by expanding %28x-4%29%283x-1%29 to get 3%2Ax%5E2-13%2Ax%2B4 or by graphing the original expression and the answer (the two graphs should be identical).

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

how to factor

The idea is to position the -4 and -1 so as SUM of the outside and the inside terms =  -13x

3x^2-13x+4 = (3x  __)(x  __) = (3x - 1)(x - 4)



                               F	First terms  3x^2

                               O	Outside terms -12x

                               I	Inside terms    -x

                               L	Last terms      4