document.write( "Question 1145140: If the polynomial p(x) = (x^5 - 6x + 7)^2019 - (x^5 - 6x + 9)^2020 + 5x^5 - 30x + 50 is divided by x^5 - 6x + 8,
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Algebra.Com's Answer #766344 by ikleyn(52891) $\"\"$ $\"About$

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document.write( "First addend,  ,  gives the remainder  (-1)^2019 = -1,  when divided by x^5 - 6x + 8.   OBVIOUSLY.\r\n" );
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document.write( "Second addend,  ,  gives the remainder  1^2020 = 1,  when divided by x^5 - 6x + 8.   OBVIOUSLY.\r\n" );
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document.write( "Third addend,  ,  gives the remainder  42,  when divided by x^5 - 6x + 8.   OBVIOUSLY.\r\n" );
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document.write( "Thus we know all three partial remainders, and are in position to answer the question now.\r\n" );
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document.write( "ANSWER.  The remainder under the question is  -1 - 1 + 42 = 40.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, answered, explained and completed.\r
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\n" ); document.write( "\n" ); document.write( "Nice problem (!) An Olympiad level (!)\r
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\n" ); document.write( "\n" ); document.write( "Thanks for posting it : it was a pleasure to me to solve it (!)\r
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\n" ); document.write( "\n" ); document.write( "Come again soon to this forum to learn something new (!)\r
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