document.write( "Question 669405: Find all zeros of the following polynomial. Write in factored form.\r
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Algebra.Com's Answer #416394 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "f(x)=7x³+x²+7x-1\r\n" );
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document.write( "That is not factorable, so I suspect there is a typo and it \r\n" );
document.write( "should have been either\r\n" );
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document.write( "f(x)=7x³-x²+7x-1  or f(x)=7x³+x²-7x-1 or f(x)=7x³+x²+7x+1\r\n" );
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document.write( "because all those are factorable by grouping, whereas the\r\n" );
document.write( "one given is not.\r\n" );
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document.write( "If it should have been\r\n" );
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document.write( "f(x)=7x³-x²+7x-1\r\n" );
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document.write( "Factor the first two terms by taking out x²\r\n" );
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document.write( "f(x)=x²(7x-1)+7x-1\r\n" );
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document.write( "Factor 1 out of the last two terms\r\n" );
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document.write( "f(x)=x²(7x-1)+1(7x-1)\r\n" );
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document.write( "Now factor out (7x-1)\r\n" );
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document.write( "f(x)=(7x-1)(x²+1)\r\n" );
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document.write( "That's in factored form\r\n" );
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document.write( "To find the zeros set each factor = 0\r\n" );
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document.write( "7x-1 =9\r\n" );
document.write( "  7x = 1\r\n" );
document.write( "   x = .  That's one zero.\r\n" );
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document.write( "x²+1 = 0\r\n" );
document.write( "  x² = -1\r\n" );
document.write( "   x = ±i\r\n" );
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document.write( "So the three zeros are , i and -i.\r\n" );
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document.write( "If it was one of the others, they're all just \r\n" );
document.write( "like this one except for + and - signs.\r\n" );
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document.write( "Edwin

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