SOLUTION: Factor completely: 185x^2 + 9x � 2 using Factoring Trinomials

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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