中四數學...有幾題唔識做啊 幫幫手

1a)
f(x) = x^99+1
f(-1) = (-1)^99 + 1
f(-1) = 0

當x^99+1除以x+1的餘數是 0

b) from (a), sub x = 6
(6^99 + 1) 除 7 的餘數是 0
(6^99) 除 7 的餘數是 6
所以若今天是星期一,則6^99日後將是星期日


2a)
f(x)=x^n+2x+3
f(-1) = (-1)^n + 2(-1) + 3
f(-1) = (-1) -2 + 3
f(-1) = 0

b) x^2-1 = (x+1)(x-1)
利用 (a)
f(-1) = 0
f(1) = 6

let the reminder be ax + b so that
f(x)=x^n+2x+3 = Q(x) * (x^2-1) + ax + b where Q(x) is the quotient
f(1)= a+b = 6 --- (1)
f(-1) = -a +b = 0 --- (2)
solving (1), (2) a = 3, b = 3
therefore the reminder is 3x + 3

3a)
x^2+x+2x(√x+2)
=x^2 + 2x(√x+2)) + x
=x^2 + 2x(√x+2)) + x + (√x+2)^2 - (√x+2)^2
=(x+(√x+2))^2 + x - (√x+2)^2
=(x+(√x+2))^2 + x - (x + 2)
=(x+(√x+2))^2 - 2


b)
x^2+x+2x(√x+2)=14
(x+(√x+2))^2 - 2 = 14
(x+(√x+2))^2 = 16
x+(√x+2) = 4 or -4 (rejected)
x = 2