Question
use the remainder theorem to find the remainder P(x)=x^(4)+9x^(3)+2x^(2)-x+5 is divided by x-2
Answers
GPT 3.5
To find the remainder of P(x) = x^4 + 9x^3 + 2x^2 - x + 5 when divided by x - 2, we can use the remainder theorem.
According to the remainder theorem, if we divide a polynomial P(x) by x - c, the remainder is equal to P(c).
So, to find the remainder, we substitute x = 2 into P(x):
P(2) = (2^4) + 9(2^3) + 2(2^2) - 2 + 5
= 16 + 72 + 8 - 2 + 5
= 99.
Therefore, the remainder when P(x) is divided by x - 2 is 99.
According to the remainder theorem, if we divide a polynomial P(x) by x - c, the remainder is equal to P(c).
So, to find the remainder, we substitute x = 2 into P(x):
P(2) = (2^4) + 9(2^3) + 2(2^2) - 2 + 5
= 16 + 72 + 8 - 2 + 5
= 99.
Therefore, the remainder when P(x) is divided by x - 2 is 99.