document.write( "Question 240748: 4,-5;\"+f%28x%29=x%5E3-6x%5E2-27x%2B140\"\r
\n" ); document.write( "\n" ); document.write( "a.x=4
\n" ); document.write( "is 4 a zero of the polynomial?\r
\n" ); document.write( "\n" ); document.write( "b.x=-5
\n" ); document.write( "is -5 a zero of the polynomial? \n" ); document.write( "
Algebra.Com's Answer #176368 by solver91311(24713)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "There are two ways to tell if a given number is a zero of a given polynomial function.\r
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\n" ); document.write( "\n" ); document.write( "First, and probably easiest conceptually, is:\r
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\n" ); document.write( "\n" ); document.write( " is a zero of the polynomial function if and only if \r
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\n" ); document.write( "\n" ); document.write( "For one of your examples:\r
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\n" ); document.write( "\n" ); document.write( " is a zero of the polynomial function if and only if .\r
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\n" ); document.write( "\n" ); document.write( "You can do your own arithmetic to check whether 4 is or is not a zero.\r
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\n" ); document.write( "\n" ); document.write( "The second method is by using Polynomial Long Division. The Polynomial Long Division method relies on the following theorem:\r
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\n" ); document.write( "\n" ); document.write( " is a zero of the polynomial function if and only if is a factor of . That is to say that there exists a polynomial function such that \r
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\n" ); document.write( "\n" ); document.write( "This leads to the process of polynomial long division. For your other example, divide by using polynomial long division. If the result is a quotient with a remainder of zero, then is a factor meaning -5 is a zero. If there is a non-zero remainder (meaning p(x) in the theorem above is a rational function rather than a polynomial function), then is NOT a factor meaning -5 is NOT a zero. \r
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\n" ); document.write( "\n" ); document.write( "Use the procedure for polynomial long division found at either of the following websites:\r
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\n" ); document.write( "\n" ); document.write( "http://www.purplemath.com/modules/polydiv2.htm\r
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\n" ); document.write( "\n" ); document.write( "or\r
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\n" ); document.write( "\n" ); document.write( "http://en.wikipedia.org/wiki/Polynomial_long_division\r
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\n" ); document.write( "\n" ); document.write( "John
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