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Use remainder theorem to find remainder when p(x) is divided by q(x) in the following question:
p(x)=x^9-5x^4+1; q(x)=x+1
GIven: $p(x)=x^9-5x^4+1; q(x)=x+1$
To do: Use remainder theorem to find the remainder when p(x) is divided by q(x)
Solution:
The remainder theorem states that when a polynomial, p(x), is divided by a linear polynomial, x - a the remainder of that division will be equivalent to p(a).
Given: $p(x) = x^9 - 5x + 1$
q (x) = x + 1
x + 1 = x -(-1)
So remainder will be p(-1):
$p (-1) = (-1)^9 - 5(-1) + 1$
= - 1 + 5 + 1
= 6 - 1
= 5
Remainder = 5
Updated on: 10-Oct-2022
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