document.write( "Question 118367: How do I find the LCM and GCF of \"x%5E3%2B10x%5E2%2B25x\" and \"x%5E4%2B5x%5E3\"? \n" ); document.write( "
Algebra.Com's Answer #86485 by Edwin McCravy(20060)\"\" \"About 
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document.write( "How do I find the LCM and GCF of\r\n" );
document.write( "\"x%5E3%2B10x%5E2%2B25x\" and \"x%5E4%2B5x%5E3\"?\r\n" );
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document.write( "You factor them all.\r\n" );
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document.write( "\"x%5E3%2B10x%5E2%2B25x\"\r\n" );
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document.write( "First take out an x\r\n" );
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document.write( "\"x%28x%5E2%2B10x%2B25%29\"\r\n" );
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document.write( "Factor the trinomial in the parentheses.\r\n" );
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document.write( "First write this:\r\n" );
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document.write( "x(x    )(x    )\r\n" );
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document.write( "Think of two whole numbers which have product\r\n" );
document.write( "+25 and sum +10.  They are +5 and +5. So the\r\n" );
document.write( "factorization is\r\n" );
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document.write( "\"x%28x+%2B+5%29%28x+%2B+5%29\"\r\n" );
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document.write( "or\r\n" );
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document.write( "\"x%28x+%2B+5%29%5E2\"\r\n" );
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document.write( "Now factor\r\n" );
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document.write( "\"x%5E4%2B5x%5E3\"\r\n" );
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document.write( "by taking out \"x%5E3\"\r\n" );
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document.write( "\"x%5E3%28x+%2B+5%29\"\r\n" );
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document.write( "Now we look at all the factors of both\r\n" );
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document.write( "\"x%28x+%2B+5%29%5E2\" and \"x%5E3%28x+%2B+5%29\"\r\n" );
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document.write( "It may help to write out the factors without exponents:\r\n" );
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document.write( "\"x%28x+%2B+5%29%28x%2B5%29\" and \"x%2Ax%2Ax%28x+%2B+5%29\"\r\n" );
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document.write( "To find the LCM. \r\n" );
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document.write( "Notice that the factor \"x\" occurs\r\n" );
document.write( "1 time in the first factor and 3 times in the second.\r\n" );
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document.write( "1 is the LEAST, so the GREATEST COMMON FACTOR contains\r\n" );
document.write( "x the LEAST number of times, which is 1 time.  \r\n" );
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document.write( "3 is the GREATEST, so the LEAST COMMON FACTOR contains \r\n" );
document.write( "x the GREATEST number of times, which is 3 times.\r\n" );
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document.write( "So far write:  \r\n" );
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document.write( "GCF = x            LCM = x³\r\n" );
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document.write( "Notice that the factor \"x%2B5\" occurs\r\n" );
document.write( "2 times in the first factor and 1 time in the second.\r\n" );
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document.write( "1 is the LEAST, so the GREATEST COMMON FACTOR contains (x-5) \r\n" );
document.write( "the LEAST number of times, which is 1 time.  \r\n" );
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document.write( "2 is the GREATEST, so the LEAST COMMON FACTOR contains (x-5) \r\n" );
document.write( "the GREATEST number of times, which is 2 times.   \r\n" );
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document.write( "So we end up with the complete GCF and LCM:  \r\n" );
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document.write( "GCF = x(x+5)       LCM = x³(x+5)\r\n" );
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document.write( "Remember: \r\n" );
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document.write( "1. To get the GREATEST common factor you use each prime factor\r\n" );
document.write( "the LEAST number of times that it appears in any expression.\r\n" );
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document.write( "2. To get the LEAST common multiple you use each prime factor \r\n" );
document.write( "the GREATEST number of times that it appears in any expression.\r\n" );
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document.write( "Edwin
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