Question

Find the remainder of the polynomial $p(x) = x^{81} + x^{21} + x^9 + x^3 + x$ when divided by ( x - 1). Explain.

Answer 1

Answer: 5

Step-by-step explanation:

Let f(x) = x-1

⇒ 0 = x - 1

⇒ x = 1

By substituting f(x) in p(x) and remainder theorem,

$1^{81} +1^{21}+1^{9}+1^{3}+1\\=1+1+1+1+1\\=5$

Therefore, the remainder is  5.

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