document.write( "Question 177236: factor completely 2x^2 – 128\r
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\n" ); document.write( "\n" ); document.write( "find all positive and negative intergers b for which the polynomial can be factored.
\n" ); document.write( " 2x^2 + bx – 15 \n" ); document.write( "

Algebra.Com's Answer #132320 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"2x%5E2-128\"$ Start with the given expression\r
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\n" ); document.write( "\n" ); document.write( " $\"2%28x%5E2-64%29\"$ Factor out the GCF $\"2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"2%28x%2B8%29%28x-8%29\"$ Factor $\"x%5E2-64\"$ to get $\"%28x%2B8%29%28x-8%29\"$ (use the difference of squares formula)\r
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\n" ); document.write( "\n" ); document.write( "So $\"2x%5E2-128\"$ completely factors to $\"2%28x%2B8%29%28x-8%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"2x%5E2-128=2%28x%2B8%29%28x-8%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "First, take the leading coefficient 2 and the last term -15 and multiply the two numbers to get $\"2%28-15%29=-30\"$ \r
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\n" ); document.write( "\n" ); document.write( "If we want this to be factorable, we need to ask the question: what two numbers multiply to -30 and add to the middle coefficient \"b\"?\r
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\n" ); document.write( "\n" ); document.write( "So let's list the factors of $\"-30\"$ :\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-5,-6,-10,-15,-30\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 $\"-30\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*(-30)
\n" ); document.write( "2*(-15)
\n" ); document.write( "3*(-10)
\n" ); document.write( "5*(-6)
\n" ); document.write( "(-1)*(30)
\n" ); document.write( "(-2)*(15)
\n" ); document.write( "(-3)*(10)
\n" ); document.write( "(-5)*(6)\r
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\n" ); document.write( "\n" ); document.write( "Now add them up. The last column represents all of the possible values of \"b\" that will make $\"2x%5E2+%2B+bx+-+15\"$ factorable.\r
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First Number	Second Number	Sum
1	-30	1+(-30)=-29
2	-15	2+(-15)=-13
3	-10	3+(-10)=-7
5	-6	5+(-6)=-1
-1	30	-1+30=29
-2	15	-2+15=13
-3	10	-3+10=7
-5	6	-5+6=1

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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So the possible values of \"b\" are: -29, -13, -7, -1, 29, 13, 7, and 1 (look at the third column of the table above) \n" ); document.write( "

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