document.write( "Question 201629: Factor completely: 185x^2 + 9x – 2
\n" ); document.write( "using Factoring Trinomials \n" ); document.write( "

Algebra.Com's Answer #151859 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "\r
\n" ); document.write( "\n" ); document.write( "Jump to Answer\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"185x%5E2%2B9x-2\"$ , we can see that the first coefficient is $\"185\"$ , the second coefficient is $\"9\"$ , and the last term is $\"-2\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"185\"$ by the last term $\"-2\"$ to get $\"%28185%29%28-2%29=-370\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"-370\"$ (the previous product) and add to the second coefficient $\"9\"$ ?\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "To find these two numbers, we need to list all of the factors of $\"-370\"$ (the previous product).\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Factors of $\"-370\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,2,5,10,37,74,185,370\r
\n" ); document.write( "\n" ); document.write( "-1,-2,-5,-10,-37,-74,-185,-370\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Note: list the negative of each factor. This will allow us to find all possible combinations.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "These factors pair up and multiply to $\"-370\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*(-370) = -370
\n" ); document.write( "2*(-185) = -370
\n" ); document.write( "5*(-74) = -370
\n" ); document.write( "10*(-37) = -370
\n" ); document.write( "(-1)*(370) = -370
\n" ); document.write( "(-2)*(185) = -370
\n" ); document.write( "(-5)*(74) = -370
\n" ); document.write( "(-10)*(37) = -370\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now let's add up each pair of factors to see if one pair adds to the middle coefficient $\"9\"$ :\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "

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

\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "From the table, we can see that there are no pairs of numbers which add to $\"9\"$ . So $\"185x%5E2%2B9x-2\"$ cannot be factored.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "===============================================================\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Answer:\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So $\"185x%5E2%2B9x-2\"$ doesn't factor at all (over the rational numbers).\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So $\"185x%5E2%2B9x-2\"$ is prime.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Jump to Top
\n" ); document.write( " \n" ); document.write( "

\n" );