document.write( "Question 93733: Hello, \r
\n" ); document.write( "\n" ); document.write( "Can you PLEASE help me?? I cannot understand how to do this! I really do appreciate all your help!!\r
\n" ); document.write( "\n" ); document.write( "Find two integers c (positive or negative) for which each polynomial can be factored.
\n" ); document.write( "x^2+x+c
\n" ); document.write( "x^2-2x+c
\n" ); document.write( "x^2-3x+c\r
\n" ); document.write( "\n" ); document.write( "Thank you in advance!!\r
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Algebra.Com's Answer #68303 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Hello, \r\n" );
document.write( "Can you PLEASE help me?? I cannot understand how to do this! I \r\n" );
document.write( "really do appreciate all your help!! \r\n" );
document.write( "Find two integers c (positive or negative) for which each \r\n" );
document.write( "polynomial can be factored.\r\n" );
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document.write( "x² + x + c\r\n" );
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document.write( "For emphasis I will put a 1 before the x:\r\n" );
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document.write( "x² + 1x + c  \r\n" );
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document.write( "That would factor if c were such that we could think of two\r\n" );
document.write( "integers which have product c and sum 1. \r\n" );
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document.write( "So, for example, we think of two integers which have sum 1, \r\n" );
document.write( "say +6 and -5, and then if c were their product, -30, it \r\n" );
document.write( "would factor.  So choose c as -30.\r\n" );
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document.write( "Checking: \r\n" );
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document.write( "x² + 1x - 30 factors as\r\n" );
document.write( "(x + 6)(x - 5)\r\n" );
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document.write( "We could have picked instead two other integers \r\n" );
document.write( "whose sum is +1.  For instance we could have picked\r\n" );
document.write( "-1 and +2, then c = (-1)(+2) = -2.\r\n" );
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document.write( "So another answer is c = -2. Checking,\r\n" );
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document.write( " x² + x - 2 factors as\r\n" );
document.write( "(x - 1)(x + 2) \r\n" );
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document.write( "There are infinitely many answers for c.\r\n" );
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document.write( "----------------------------\r\n" );
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document.write( "x² - 2x + c\r\n" );
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document.write( "We do it the exact same way.\r\n" );
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document.write( "That would factor if c were such that we could think of two\r\n" );
document.write( "integers which have product c and sum -2.  So we think of two\r\n" );
document.write( "integers which have sum -2, say -8 and +6, and then if c were\r\n" );
document.write( "their product, -48, it would factor.  So choose c as -48.\r\n" );
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document.write( "Checking: \r\n" );
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document.write( "x² - 2x - 48 factors as\r\n" );
document.write( "(x - 8)(x + 6)\r\n" );
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document.write( "We could have picked instead two other integers \r\n" );
document.write( "whose sum is -2.  For instance we could have picked\r\n" );
document.write( "+5 and -7, then c = (+5)(-7) = -35.\r\n" );
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document.write( "So another answer is c = -35. Checking,\r\n" );
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document.write( " x² + x - 35 factors as\r\n" );
document.write( "(x + 5)(x - 7) \r\n" );
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document.write( "As in all such problems, there are infinitely many \r\n" );
document.write( "answers for c.\r\n" );
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document.write( "x² - 3x + c\r\n" );
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document.write( "I'll leave that one for you to do. Just think of two\r\n" );
document.write( "numbers that have sum -3, say -2 and -1, or -8 and +5, \r\n" );
document.write( "or -53 and +50, or -4 and +1, or -103 and 100, \r\n" );
document.write( "or -999999999 and +999999996, J or .......\r\n" );
document.write( "Then multiply them together to find a value for c.\r\n" );
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document.write( "Edwin
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