document.write( "Question 169026: b^2+3b+18\r
\n" ); document.write( "\n" ); document.write( "is this prime yes or no? \n" ); document.write( "

Algebra.Com's Answer #124671 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"b%5E2%2B3b%2B18\"$ , we can see that the first coefficient is $\"1\"$ , the second coefficient is $\"3\"$ , and the last term is $\"18\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"1\"$ by the last term $\"18\"$ to get $\"%281%29%2818%29=18\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"18\"$ (the previous product) and add to the second coefficient $\"3\"$ ?\r
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\n" ); document.write( "\n" ); document.write( "To find these two numbers, we need to list all of the factors of $\"18\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"18\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,2,3,6,9,18\r
\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-6,-9,-18\r
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\n" ); document.write( "\n" ); document.write( "Note: list the negative of each factor. This will allow us to find all possible combinations.\r
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\n" ); document.write( "\n" ); document.write( "These factors pair up and multiply to $\"18\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*18
\n" ); document.write( "2*9
\n" ); document.write( "3*6
\n" ); document.write( "(-1)*(-18)
\n" ); document.write( "(-2)*(-9)
\n" ); document.write( "(-3)*(-6)\r
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\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 $\"3\"$ :\r
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First Number	Second Number	Sum
1	18	1+18=19
2	9	2+9=11
3	6	3+6=9
-1	-18	-1+(-18)=-19
-2	-9	-2+(-9)=-11
-3	-6	-3+(-6)=-9

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that there are no pairs of numbers which add to $\"3\"$ . So $\"b%5E2%2B3b%2B18\"$ cannot be factored.\r
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\n" ); document.write( "\n" ); document.write( "So $\"b%5E2%2B3b%2B18\"$ is prime. \n" ); document.write( "

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