document.write( "Question 1196286: The remainder when 𝑝(𝑥) = 𝑥^2022 − 𝑥^2021 + 𝑥^2020 − ⋯ + (−1)^𝑖𝑥^𝑖 + ⋯ −𝑥^3 + 𝑥^2 − 𝑥 + 1, is divided by (𝑥 − 1) is \n" ); document.write( "

Algebra.Com's Answer #829050 by ikleyn(52788) $\"\"$ $\"About$

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document.write( "Due to the Remainder theorem, the remainder of division is the value of the polynomial p(x) at x= 1.\r\n" );
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document.write( "So, substitute x= 1 into the polynomial and calculate the obtained alternate sum.\r\n" );
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document.write( "Since the degree 2002 is an even number, the number of  \" + 1 \"  addends  will be one more \r\n" );
document.write( "than the number of  \" -1 \"  addends, so the alternate sum is 1 (one).\r\n" );
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document.write( "ANSWER.  The remainder is 1.\r\n" );
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