document.write( "Question 1079554: Determine whether the statement is true or false.\r
\n" ); document.write( "\n" ); document.write( "If x - 3 is a factor of a polynomial f(x), then f(-3) = 0. \n" ); document.write( "

Algebra.Com's Answer #693818 by ikleyn(52794) $\"\"$ $\"About$

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document.write( "1.  This statement, as it presented in the post, might be TRUE and MIGHT be FALSE,\r\n" );
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document.write( "    DEPENDING on the polynomial f(x).\r\n" );
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document.write( "    For example,  if f(x) = , then (x-3) is the factor of f(x), but f(-3) =  =  = 36 is not zero.\r\n" );
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document.write( "    From the other side, if f(x) = (x-3)*(x+3), then (x-3) is the factor of f(x), and f(-3) = (3-(-3))*(3+(-3)) = 0.\r\n" );
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document.write( "2.  But, if I modify the statement in this way:\r\n" );
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document.write( "         Determine whether the statement is true or false.\r\n" );
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document.write( "              If x - 3 is a factor of a polynomial f(x), then f(3) = 0\r\n" );
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document.write( "    then this MODIFIED statement is TRUE.\r\n" );
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document.write( "    It follows from the \"Remainder theorem\".\r\n" );
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\n" ); document.write( "\n" ); document.write( "On \"Remainder theorem\" see the lesson \r
\n" ); document.write( "\n" ); document.write( " - Divisibility of polynomial f(x) by binomial (x-a). The Remainder theorem\r
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