document.write( "Question 635633: Hi, I know I know this, but I am drawing a blank, and could use some help please.\r
\n" ); document.write( "\n" ); document.write( "Factor completely. 9x^5-45x^4+27x^3.\r
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Algebra.Com's Answer #400438 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "\"9x%5E5-45x%5E4%2B27x%5E3\" Start with the given expression.\r
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\n" ); document.write( "\n" ); document.write( "\"9x%5E3%28x%5E2-5x%2B3%29\" Factor out the GCF \"9x%5E3\".\r
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\n" ); document.write( "\n" ); document.write( "Now let's try to factor the inner expression \"x%5E2-5x%2B3\"\r
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\n" ); document.write( "\n" ); document.write( "Looking at the expression \"x%5E2-5x%2B3\", we can see that the first coefficient is \"1\", the second coefficient is \"-5\", and the last term is \"3\".\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient \"1\" by the last term \"3\" to get \"%281%29%283%29=3\".\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to \"3\" (the previous product) and add to the second coefficient \"-5\"?\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 \"3\" (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of \"3\":\r
\n" ); document.write( "\n" ); document.write( "1,3\r
\n" ); document.write( "\n" ); document.write( "-1,-3\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 \"3\".\r
\n" ); document.write( "\n" ); document.write( "1*3 = 3
\n" ); document.write( "(-1)*(-3) = 3\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 \"-5\":\r
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First NumberSecond NumberSum
131+3=4
-1-3-1+(-3)=-4
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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 \"-5\". So \"x%5E2-5x%2B3\" cannot be factored.\r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So \"9x%5E5-45x%5E4%2B27x%5E3\" simply factors to \"9x%5E3%28x%5E2-5x%2B3%29\"\r
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\n" ); document.write( "\n" ); document.write( "In other words, \"9x%5E5-45x%5E4%2B27x%5E3=9x%5E3%28x%5E2-5x%2B3%29\".
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