document.write( "Question 743612: How do I factor, 10a^3+9a^2+2a. I know that it converts to: (10a^3 +5a^2)+ (4a^2 +2a)But i am not sure what to do next. \n" ); document.write( "
Algebra.Com's Answer #452982 by Edwin McCravy(20060)\"\" \"About 
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document.write( "10a³ + 9a² + 2a\r\n" );
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document.write( "Factor out \"a\"\r\n" );
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document.write( "a(10a² + 9a + 2)\r\n" );
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document.write( "Now we'll factor  10a² + 9a + 2 \r\n" );
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document.write( "Multiply the 10 by the 2, get 20\r\n" );
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document.write( "Write down all the ways to have two positive integers\r\n" );
document.write( "which have product 20, starting with 20*1\r\n" );
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document.write( "20*1\r\n" );
document.write( "10*2\r\n" );
document.write( " 5*4\r\n" );
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document.write( "Since the last sign in 10a² + 9a + 2 is +, ADD them,\r\n" );
document.write( "and place the SUM out beside that:\r\n" );
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document.write( " 20*1   20+1=21\r\n" );
document.write( " 10*2   10+2=12\r\n" );
document.write( "  5*4    5+4=9\r\n" );
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document.write( "Now, again ignoring signs, we find in that list of\r\n" );
document.write( "sums the coefficient of the middle term in 10a² + 9a + 2\r\n" );
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document.write( "So we replace the number 9 by 5+4\r\n" );
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document.write( "10a² + 9a + 2\r\n" );
document.write( "10a² + (5+4)a + 2\r\n" );
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document.write( "Then we distribute to remove the parentheses:\r\n" );
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document.write( "10a² + 5a + 4a + 2\r\n" );
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document.write( "Factor the first two terms 10a² + 5a by taking out the\r\n" );
document.write( "greatest common factor, getting 5a(2a + 1)\r\n" );
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document.write( "Factor the last two terms +4a + 2 by taking out the\r\n" );
document.write( "greatest common factor, +2, getting +2(2a + 1)\r\n" );
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document.write( "So we have\r\n" );
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document.write( "5a(2a + 1) + 2(2a + 1) \r\n" );
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document.write( "Notice that there is a common factor, (2a + 1)\r\n" );
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document.write( "5a(2a + 1)+ 2(2a + 1)\r\n" );
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document.write( "which we can factor out leaving the 5a and the +2 to put \r\n" );
document.write( "in parentheses:\r\n" );
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document.write( "(2a + 1)(5a + 2)\r\n" );
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document.write( "Now remember there was an \"a\" factor in front that\r\n" );
document.write( "we took out first\r\n" );
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document.write( "a(10a² + 9a + 2)\r\n" );
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document.write( "So the answer is:\r\n" );
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document.write( "a(2a + 1)(5a + 2)\r\n" );
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document.write( "Edwin
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