SOLUTION: How do you factor 4m^2 +14m +1

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Question 719352: How do you factor 4m^2 +14m +1
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 4x%5E2%2B14x%2B1, we can see that the first coefficient is 4, the second coefficient is 14, and the last term is 1.



Now multiply the first coefficient 4 by the last term 1 to get %284%29%281%29=4.



Now the question is: what two whole numbers multiply to 4 (the previous product) and add to the second coefficient 14?



To find these two numbers, we need to list all of the factors of 4 (the previous product).



Factors of 4:

1,2,4

-1,-2,-4



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



These factors pair up and multiply to 4.

1*4 = 4
2*2 = 4
(-1)*(-4) = 4
(-2)*(-2) = 4


Now let's add up each pair of factors to see if one pair adds to the middle coefficient 14:



First NumberSecond NumberSum
141+4=5
222+2=4
-1-4-1+(-4)=-5
-2-2-2+(-2)=-4




From the table, we can see that there are no pairs of numbers which add to 14. So 4x%5E2%2B14x%2B1 cannot be factored.



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Answer:



So 4%2Ax%5E2%2B14%2Ax%2B1 doesn't factor at all (over the rational numbers).



So 4%2Ax%5E2%2B14%2Ax%2B1 is prime.