SOLUTION: I need help factoring this, i have tried and can't figure it out.. the problem is 49x^2-42x+5 Thank You

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Question 411232: I need help factoring this, i have tried and can't figure it out..
the problem is 49x^2-42x+5

Thank You
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

49x%5E2-42x%2B5

Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)


Looking at the expression 49x%5E2-42x%2B5, we can see that the first coefficient is 49, the second coefficient is -42, and the last term is 5.



Now multiply the first coefficient 49 by the last term 5 to get %2849%29%285%29=245.



Now the question is: what two whole numbers multiply to 245 (the previous product) and add to the second coefficient -42?



To find these two numbers, we need to list all of the factors of 245 (the previous product).



Factors of 245:

1,5,7,35,49,245

-1,-5,-7,-35,-49,-245



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



These factors pair up and multiply to 245.

1*245 = 245
5*49 = 245
7*35 = 245
(-1)*(-245) = 245
(-5)*(-49) = 245
(-7)*(-35) = 245


Now let's add up each pair of factors to see if one pair adds to the middle coefficient -42:



First NumberSecond NumberSum
12451+245=246
5495+49=54
7357+35=42
-1-245-1+(-245)=-246
-5-49-5+(-49)=-54
-7-35-7+(-35)=-42




From the table, we can see that the two numbers -7 and -35 add to -42 (the middle coefficient).



So the two numbers -7 and -35 both multiply to 245 and add to -42



Now replace the middle term -42x with -7x-35x. Remember, -7 and -35 add to -42. So this shows us that -7x-35x=-42x.



49x%5E2%2Bhighlight%28-7x-35x%29%2B5 Replace the second term -42x with -7x-35x.



%2849x%5E2-7x%29%2B%28-35x%2B5%29 Group the terms into two pairs.



7x%287x-1%29%2B%28-35x%2B5%29 Factor out the GCF 7x from the first group.



7x%287x-1%29-5%287x-1%29 Factor out 5 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.



%287x-5%29%287x-1%29 Combine like terms. Or factor out the common term 7x-1



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Answer:



So 49%2Ax%5E2-42%2Ax%2B5 factors to %287x-5%29%287x-1%29.



In other words, 49%2Ax%5E2-42%2Ax%2B5=%287x-5%29%287x-1%29.



Note: you can check the answer by expanding %287x-5%29%287x-1%29 to get 49%2Ax%5E2-42%2Ax%2B5 or by graphing the original expression and the answer (the two graphs should be identical).