document.write( "Question 1009653: f(x) = x^4 - x^3 - 4^x2 +4 find factor completely. then graph it
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\n" ); document.write( "\n" ); document.write( "f(x) = (x^3 - 4x - 4)(x-1) but i don't know how to graph this. Please help. Thank you. \n" ); document.write( "
Algebra.Com's Answer #625119 by Edwin McCravy(20060)\"\" \"About 
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document.write( "f(x) = x^4 - x^3 - 4^x2 +4 \r\n" );
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document.write( "By DesCartes' rule of signs it has 2 sign changes so it\r\n" );
document.write( "has 2 or 0 positive real zeros.\r\n" );
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document.write( "We know by the factored form \r\n" );
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document.write( "f(x) = (x^3 - 4x - 4)(x-1)\r\n" );
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document.write( "That it has at least 1 positive real zero, 1, so by DesCartes' \r\n" );
document.write( "rule of signs, it MUST have 2 positive real zeros. \r\n" );
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document.write( "We know since 1 has multiplicity 1 that the curve cuts\r\n" );
document.write( "through the x-axis there.\r\n" );
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document.write( "We know it goes up on the far right because the leading\r\n" );
document.write( "coefficient 1 of 1x^4 is positive.  We know that it also goes \r\n" );
document.write( "up on the far left also because the degree 4 is even.\r\n" );
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document.write( "We make a table of 5 values:\r\n" );
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document.write( " x | y\r\n" );
document.write( "-2 | 12\r\n" );
document.write( "-1 | 2\r\n" );
document.write( " 0 | 4\r\n" );
document.write( " 2 |-4\r\n" );
document.write( " 3 |22 \r\n" );
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document.write( "We plot those points:\r\n" );
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document.write( "So the graph must look something like this:\r\n" );
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document.write( "Edwin
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