document.write( "Question 470046: Find all solutions, real or complex, to the following equation\r
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Algebra.Com's Answer #322469 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "  x³-4x²-9x+36\r\n" );
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document.write( "You called that an equation, but there is no equal sign, so\r\n" );
document.write( "it isn't an equation.  Was it supposed to have = 0 after it\r\n" );
document.write( "like this?:\r\n" );
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document.write( "  x³-4x²-9x+36 = 0\r\n" );
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document.write( "Then it would have been an equation to solve.  But if it\r\n" );
document.write( "is only\r\n" );
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document.write( "  x³-4x²-9x+36\r\n" );
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document.write( "then we can only factor it, not solve it.  \r\n" );
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document.write( "First I will assume there was no = 0 after it and the \r\n" );
document.write( "instructions were not to solve the equation but to \r\n" );
document.write( "factor the expression\r\n" );
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document.write( "Factor the first two terms x³-4x² by taking out the\r\n" );
document.write( "greatest common factor, x², getting x²(x-4)\r\n" );
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document.write( "Factor the last two terms -9x+36 by taking out the\r\n" );
document.write( "greatest common factor, getting -9(x-4)\r\n" );
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document.write( "So we have\r\n" );
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document.write( "x²(x-4)-9(x-4)\r\n" );
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document.write( "Notice that there is a common factor, (x-4)\r\n" );
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document.write( "x²(x-4)-9(x-4)\r\n" );
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document.write( "which we can factor out leaving the x² and the -9 to put \r\n" );
document.write( "in parentheses:\r\n" );
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document.write( "(x-4)(x²-9)\r\n" );
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document.write( "Notice that the (x²-9) is the difference of two perfect squares\r\n" );
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document.write( "So the final factorization is\r\n" );
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document.write( "(x-4)(x-3)(x+3)\r\n" );
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document.write( "That's the final answer if the instructions were \"factor the \r\n" );
document.write( "expression\".\r\n" );
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document.write( "However if it was an equation as you stated and there was an equal \r\n" );
document.write( "sign and a 0 after it, like this:\r\n" );
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document.write( "(x-4)(x-3)(x+3) = 0\r\n" );
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document.write( "then we use the zero factor principle:\r\n" );
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document.write( "x-4=0   x-3=0   x+3=0\r\n" );
document.write( "  x=4     x=3     x=-3\r\n" );
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document.write( "Then there are three solutions to the equation, and\r\n" );
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document.write( "they are 4,3,and -3.\r\n" );
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document.write( "Edwin
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