document.write( "Question 78620: factor the polynomial completely,clearly show GCF\r
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Algebra.Com's Answer #56357 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "factor the polynomial completely,clearly show GCF \r\n" );
document.write( "4x² - 16 \r\n" );
document.write( "I went another step and I am not sure weather \r\n" );
document.write( "to factor again after this: \r\n" );
document.write( "(2x - 4)(2x + 4)\r\n" );
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document.write( "What you did was mathematically correct, but \r\n" );
document.write( "the result is not simplified.\r\n" );
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document.write( "You skipped the first step which should always\r\n" );
document.write( "be done first.\r\n" );
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document.write( "Before looking for any other factoring method, \r\n" );
document.write( "always look for a common factor.\r\n" );
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document.write( "In doing your problem\r\n" );
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document.write( "    4x² - 16\r\n" );
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document.write( "You should first have noticed that there is \r\n" );
document.write( "a common factor of 4.  You should have done \r\n" );
document.write( "that first. Then you would have\r\n" );
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document.write( "   4(x² - 4)\r\n" );
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document.write( "Then you would factor the expression in the\r\n" );
document.write( "parentheses as the difference of two squares\r\n" );
document.write( "and the final answer would have been:\r\n" );
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document.write( "  4(x - 2)(x + 2).\r\n" );
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document.write( "Now what you did was skip the first step and\r\n" );
document.write( "factor the original problem as the difference\r\n" );
document.write( "of two squares, and got\r\n" );
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document.write( "  (2x - 4)(2x + 4)\r\n" );
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document.write( "That can be factored further but it takes more\r\n" );
document.write( "steps than if you had factored out the 4 first:\r\n" );
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document.write( "Factor out 2 in the first parentheses:\r\n" );
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document.write( " 2(x - 2)(2x + 4)\r\n" );
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document.write( "Now factor out 2 in the second parentheses:\r\n" );
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document.write( " 2(x - 2)2(x + 2)\r\n" );
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document.write( "Now multiply the 2's together and get\r\n" );
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document.write( " 4(x - 2)(x + 2)\r\n" );
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document.write( "Although that is correct it is going about \r\n" );
document.write( "it the long way.\r\n" );
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document.write( "ALWAYS look for a common factor FIRST!\r\n" );
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document.write( "[Incidentally you originally had \"(2x-4)(2x-4)\".\r\n" );
document.write( "not (2x-4)(2x+4). I assumed that was a typo \r\n" );
document.write( "and so I corrected it. I assumed you knew that \r\n" );
document.write( "the sign in the second parentheses should have\r\n" );
document.write( "been +, not -.  If you thought they should both \r\n" );
document.write( "be -, learn now that one sign is - and the \r\n" );
document.write( "other is +.]\r\n" );
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document.write( "Edwin

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