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Question 201629: Factor completely: 185x^2 + 9x – 2
using Factoring Trinomials
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
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Looking at the expression  , we can see that the first coefficient is  , the second coefficient is  , and the last term is  .
Now multiply the first coefficient by the last term to get  .
Now the question is: what two whole numbers multiply to  (the previous product) and add to the second coefficient ?
To find these two numbers, we need to list all of the factors of (the previous product).
Factors of :
1,2,5,10,37,74,185,370
-1,-2,-5,-10,-37,-74,-185,-370
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to .
1*(-370) = -370
2*(-185) = -370
5*(-74) = -370
10*(-37) = -370
(-1)*(370) = -370
(-2)*(185) = -370
(-5)*(74) = -370
(-10)*(37) = -370
Now let's add up each pair of factors to see if one pair adds to the middle coefficient :
| First Number | Second Number | Sum | | 1 | -370 | 1+(-370)=-369 | | 2 | -185 | 2+(-185)=-183 | | 5 | -74 | 5+(-74)=-69 | | 10 | -37 | 10+(-37)=-27 | | -1 | 370 | -1+370=369 | | -2 | 185 | -2+185=183 | | -5 | 74 | -5+74=69 | | -10 | 37 | -10+37=27 |
From the table, we can see that there are no pairs of numbers which add to . So cannot be factored.
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Answer:
So doesn't factor at all (over the rational numbers).
So is prime.
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