document.write( "Question 204273: Find the remainder when $\"3x%5E100%2B5x%5E85-4x%5E38%2B2x%5E17-6\"$ is divide by x+1 \n" ); document.write( "

Algebra.Com's Answer #154253 by RAY100(1637) $\"\"$ $\"About$

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It is easy to divide a polynomial by (x+1), however with exponents of 100, it becomes tedious, as all exponents must be \"filled in\" to make algorithm work.
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\n" ); document.write( "However, The REMAINDER THEOREM states,\" if a polynomial,f(x) is divided by
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\n" ); document.write( "given (x+1) = (x-k),,,k=(-1)
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\n" ); document.write( "To find remainder, evaluate, f(-1), that is substitute (-1) for (x)
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\n" ); document.write( "f(-1) = 3(-1)^100 +5(-1)^85 -4(-1)^38 +2(-1)^17 -6
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\n" ); document.write( "f(-1) = +3(1)+5(-1)-4(1) +2(-1) -6
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\n" ); document.write( "f(-1) = -14,,,,,and REMAINDER = (-14)
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