What is the remainder when the polynomial $p ( x ) = 7 x ^ { 500 } - 43 x ^ { 56 } - 3 x ^ { 4 } - 1$ is divided by $( x + 1 )$
?
A) $- 1$
B) $500$
C) $- 40$
D) $- 556$
E) $1$

Question

Quizplus · Accepted Answer

By the Remainder Theorem, the remainder of a polynomial $p(x)$ divided by $x - a$ is $p(a)$. Here, $a = -1$, so we calculate $p(-1) = 7(-1)^{500} - 43(-1)^{56} - 3(-1)^{4} - 1 = 7 - 43 - 3 - 1 = -40$.

What Is the Remainder When the Polynomial p(x)=7x500−43x56−3x4−1p ( x ) = 7 x ^ { 500 } - 43 x ^ { 56 } - 3 x ^ { 4 } - 1p(x)=7x500−43x56−3x4−1

What Is the Remainder When the Polynomial $p ( x ) = 7 x ^ { 500 } - 43 x ^ { 56 } - 3 x ^ { 4 } - 1$