1974 AHSME Problems/Problem 4: Difference between revisions

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What is the remainder when $x^{51}+51$ is divided by $x+1$ ?

$\mathrm{(A)\ } 0 \qquad \mathrm{(B) \ }1 \qquad \mathrm{(C) \ } 49 \qquad \mathrm{(D) \ } 50 \qquad \mathrm{(E) \ }51$

From the Remainder Theorem, the remainder when $x^{51}+51$ is divided by $x+1$ is $(-1)^{51}+51=-1+51=50, \boxed{\text{D}}$ .

~ pi_is_3.14

1974 AHSME (Problems • Answer Key • Resources)
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All AHSME Problems and Solutions

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 ==Solution==
 From the [[Remainder Theorem]], the remainder when <math> x^{51}+51 </math> is divided by <math> x+1 </math> is <math> (-1)^{51}+51=-1+51=50, \boxed{\text{D}} </math>.
+== Video Solution by OmegaLearn ==
+https://youtu.be/Dp-pw6NNKRo?t=256
+~ pi_is_3.14
 ==See Also==