✔ 最佳答案
1(a)
f(x) = x^1000+6
x^1000+6除以x+1的餘數 = f(-1) = -1^1000 + 6 = 1 + 6 = 7
(b) (i) x=8
8^1000 +6 除以 9(=8+1)的餘數 = 7
(ii)
8^1000 +6 除以 9的餘數 = 7
8^1000 +6-6 除以 9的餘數 = 7-6
8^1000 除以 9的餘數 = 1
2
g(x) = x^3-x^2-3x-1
g(-1)=(-1)^3-(-1)^2-3(-1)-1=-1-1+3-1=0
x^3-x^2-3x-1 除以 x+1的餘數=0
..............1 -2 -1
.......____________
1+1 ) 1 - 1 - 3 - 1
........1+1
.............-2 - 3
.............-2 -2
...................-1 - 1
x^3-x^2-3x-1 = 0
(x+1)*(1*x^2 -2*x -1) = 0
x= -1
or
x^2 - 2*x -1 = 0
x=[2+sq root((-2)^2 -(4)(-1))] / 2 or x=[2-sq root((-2)^2 -(4)(-1))] / 2
x=[2+sq root(8)] / 2 or x=[2-sq root(8)] / 2
x=[2+2*sq root(2)] / 2 or x=[2-2*sq root(2)] / 2
x=1+*sq root(2) or x=1-sq root(2)