document.write( "Question 1084384: Use the remainder theorem to determine whether x - 2 is a factor of
\n" ); document.write( "f(x) = x^3 + 3x^2 - x - 18 \n" ); document.write( "
Algebra.Com's Answer #698483 by ikleyn(52782)\"\" \"About 
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document.write( "     The binomial  \"x-a\"  divides the polynomial  \"f%28x%29\"  if and only if the value of  \"a\"  is the root of the polynomial  \"f%28x%29\",  i.e.  \"f%28a%29+=+0\".\r\n" );
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\n" ); document.write( "\n" ); document.write( "So,  to check if  (x-2)  is the factor of  f(x) = x^3 + 3x^2 - x - 18,  we need to calculate the value  f(2). \r
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\n" ); document.write( "\n" ); document.write( "It is  f(2) = \"2%5E3+%2B+3%2A2%5E2+-+x+-+18\" = 8 + 3*4 - 2 - 18 = 0.\r
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\n" ); document.write( "\n" ); document.write( "Thus according to the Remainder Theorem  (x-2)  is the factor of the given polynomial  f(x).\r
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\n" ); document.write( "   Theorem   (the remainder theorem)\r
\n" ); document.write( "\n" ); document.write( "   1. The remainder of division the polynomial  \"f%28x%29\"  by the binomial  \"x-a\"  is equal to the value  \"f%28a%29\"  of the polynomial. \r
\n" ); document.write( "\n" ); document.write( "   2. The binomial  \"x-a\"  divides the polynomial  \"f%28x%29\"  if and only if the value of  \"a\"  is the root of the polynomial  \"f%28x%29\",  i.e.  \"f%28a%29+=+0\".\r
\n" ); document.write( "\n" ); document.write( "   3. The binomial  \"x-a\"  factors the polynomial  \"f%28x%29\"  if and only if the value of  \"a\"  is the root of the polynomial  \"f%28x%29\",  i.e.  \"f%28a%29+=+0\".\r
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\n" ); document.write( "\n" ); document.write( "See the lesson\r
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\n" ); document.write( "\n" ); document.write( "Also,  you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic
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