document.write( "Question 138173: Use the Rational Zero Theorem to list all possible rational zeros for the given functions.\r
\n" ); document.write( "\n" ); document.write( "f(x)=x^4+3x^3-4x^2+5x-12 \n" ); document.write( "

Algebra.Com's Answer #100913 by solver91311(24713) $\"\"$ $\"About$

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If a polynomial $\"P%28x%29\"$ has a zero $\"p%2Fq\"$ , meaning that $\"P%28p%2Fq%29=0\"$ , then p is a factor of the constant term and q is a factor of the lead coefficient.\r
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\n" ); document.write( "\n" ); document.write( "The lead coefficient is 1 in this case, so your problem is greatly simplified -- i.e., we are guaranteed that $\"p%2Fq\"$ is an integer.\r
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\n" ); document.write( "\n" ); document.write( "You need all the possible factors of the constant term, -12, remembering to include both the positive and negative of the possible factors.\r
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\n" ); document.write( "\n" ); document.write( "1 and -1 are factors of -12
\n" ); document.write( "12 and -12 are factors of -12
\n" ); document.write( "2 and -2 are factors of -12\r
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\n" ); document.write( "\n" ); document.write( "I'll leave it to you to complete the list. \n" ); document.write( "

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