document.write( "Question 1136794: Find the remainder if the polynomial 3x^100+5x^95-4x^38+2x^17 is divided by x+1 \n" ); document.write( "

Algebra.Com's Answer #754619 by ikleyn(52817) $\"\"$ $\"About$

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document.write( "Substitute the value of x = -1 into the polynomial.\r\n" );
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document.write( "The value of the polynomial then will give you the remainder\r\n" );
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document.write( "    3*(-1)^100 + 5*(-1)^95 - 4*(-1)^38 + 2*(-1)^17 = 3*1 + 5*(-1) - 4*1 + 2*(-1) = 3 - 5 - 4 - 2 = -8.     ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "It is based on the Remainder Theorem.\r
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\n" ); document.write( "\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 lessons\r
\n" ); document.write( "\n" ); document.write( "    - Divisibility of polynomial f(x) by binomial x-a and the Remainder theorem\r
\n" ); document.write( "\n" ); document.write( "    - Solved problems on the Remainder thoerem\r
\n" ); document.write( "\n" ); document.write( "in this site.\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
\n" ); document.write( "\"Divisibility of polynomial f(x) by binomial (x-a). The Remainder theorem\".\r
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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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\n" ); document.write( "\n" ); document.write( "Do not forget to post your \"THANKS\" to me every time you get a solution from me.\r
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