document.write( "Question 1132054: Show that (x-2) is a factor of f(x) = x³-2x²-4x+8.
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Algebra.Com's Answer #748924 by ikleyn(52946)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "This problem is to use the \"Remainder theorem\".\r\n" );
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document.write( "The Remainder theorem says that the binomial (x-a) is a factor of a polynomial\r\n" );
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document.write( "    f(x) = \"a%5B0%5D%2Ax%5En+%2B+a%5B1%5D%2Ax%5E%28n-1%29+%2B+ellipsis+%2B+a%5Bn-1%5D%2Ax+%2B+a%5Bn%5D\"\r\n" );
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document.write( "if and only if the value of \"a\" is the root of the polynomial f(x), i.e. f(a) = 0.\r\n" );
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document.write( "So, in your case, to show that (x-2) is a factor of the given polynomial \r\n" );
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document.write( "    f(x) = \"x%5E3+-+2x%5E2+-+4x+%2B+8\",\r\n" );
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document.write( "you need simply calculate\r\n" );
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document.write( "    f(5) = \"2%5E3+-+2%2A2%5E2+-+4%2A2+%2B+8\" = 8 - 8 - 8 + 8 = 0\r\n" );
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document.write( "and make sure that it is equal to zero.\r\n" );
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\n" ); document.write( "\n" ); document.write( "See the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Divisibility of polynomial f(x) by binomial x-a and the Remainder theorem\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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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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