### + / -檢視主題

X^2000 除以 X^3+2x^2+2x+1 ,求餘式?
X^3+2x^2+2x+1=(x+1)(x^2+x+1)

f(-1)=1

f(x)=x^2000=(x^3)^666*(x^2)

=>x^2000=(x^3-1)K(x)+x^2=(x^3-1)K(x)+(x^2+x+1)+(-x-1)
f(x)=(x+1)(x^2+x+1)P(x)+a(x^2+x+1)+(-x-1)
f(-1)=a(1-1+1)-(-1)-1=1
=>a=1
f(x)=(x+1)(x^2+x+1)P(x)+(x^2+x+1)+(-x-1)
=(x+1)(x^2+x+1)P(x)+x^2

### [數學]94年台南女中數學科教甄考題

#ed_op#DIV#ed_cl##ed_op#SPAN class=postbody#ed_cl#初試分為兩部分 #ed_op#BR#ed_cl##ed_op#BR#ed_cl#一.資訊能力檢測(5%) #ed_op#BR#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#SPAN class=postbody#ed_cl#1.給你一份試卷要妳用word打出來 #ed_op#BR#ed_cl##ed_op#/DIV#ed_cl##ed_op#/SPAN#ed_cl##ed_op#DIV#ed_cl##ed_op#SPAN class=postbody#ed_cl#2.給妳各學生各次段考的成績.要你用excel打出並算出 #ed_op#BR#ed_cl#平均和繪製各學生各次段考成績的折線圖 #ed_op#BR#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#SPAN class=postbody#ed_cl#3.要你作兩頁的ppt介紹麻省理工學院網站 #ed_op#BR#ed_cl##ed_op#BR#ed_cl#二.專業科目(25%)(1-5每題5分,6-10每題15分) #ed_op#BR#ed_cl##ed_op#/DIV#ed_cl##ed_op#/SPAN#ed_cl##ed_op#DIV#ed_cl##ed_op#SPAN class=postbody#ed_cl#1.求曲線 根號[(x+4)#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#+(y-3)#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#]-根號[(x-4)#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#+(y+3)#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#]=8 之正焦弦長 #ed_op#BR#ed_cl##ed_op#/DIV#ed_cl##ed_op#/SPAN#ed_cl##ed_op#DIV#ed_cl##ed_op#SPAN class=postbody#ed_cl#2.P是1的三次方根,Q是1的四次方根,P和Q不等於1,在複數平面上,O為原點, #ed_op#BR#ed_cl#求三角形OPQ面積最大為? #ed_op#BR#ed_cl##ed_op#/DIV#ed_cl##ed_op#/SPAN#ed_cl##ed_op#DIV#ed_cl##ed_op#SPAN class=postbody#ed_cl#3.直線L經[4 0]轉換後得到直線L':3x+4y-12=0 , 求L的方程式? #ed_op#BR#ed_cl#[0 3] #ed_op#BR#ed_cl##ed_op#/DIV#ed_cl##ed_op#/SPAN#ed_cl##ed_op#DIV#ed_cl##ed_op#SPAN class=postbody#ed_cl#4.甲乙丙丁進行比賽,若同分則名次相同,則有多少種不同排名 #ed_op#BR#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#SPAN class=postbody#ed_cl#5.X#ed_op#SUP#ed_cl#2000#ed_op#/SUP#ed_cl# 除以 X#ed_op#SUP#ed_cl#3#ed_op#/SUP#ed_cl#+2x#ed_op#SUP#ed_cl#2#ed_op#/SUP#ed_cl#+2x+1 ,求餘式? #ed_op#BR#ed_cl##ed_op#/DIV#ed_cl##ed_op#/SPAN#ed_cl##ed_op#DIV#ed_cl##ed_op#SPAN class=postbody#ed_cl#6.(1)代數基本定理 #ed_op#BR#ed_cl#(2)最適合直線(回歸直線) #ed_op#BR#ed_cl#(3)多面體的尤拉定理 #ed_op#BR#ed_cl#(4)直角三角形畢氏定理在四面體中的的推廣 #ed_op#BR#ed_cl#(5)圓內接四邊形"Ptolemy"定理 #ed_op#BR#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#SPAN class=postbody#ed_cl#7.導出空間一點P(Xo,Yo,Zo)到平面aX+bY+cZ+d=0的距離 #ed_op#BR#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#SPAN class=postbody#ed_cl#8.凸四邊形四邊長分別為a,b,c,d,對角線所夾銳角45度,以a,b,c,d表四邊形面積. #ed_op#BR#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#SPAN class=postbody#ed_cl#9.找出所有正整數m,n 使得(m+n)#ed_op#SUP#ed_cl#m#ed_op#/SUP#ed_cl#=n#ed_op#SUP#ed_cl#m#ed_op#/SUP#ed_cl#+1413 #ed_op#BR#ed_cl#10.求所有函數f(x),對任意實數x(|x|不等於1),滿足 #ed_op#BR#ed_cl#　x-3　　 3+x #ed_op#BR#ed_cl#f(-----) + f(-----) = x #ed_op#BR#ed_cl#　x+1 　　1-x#ed_op#BR#ed_cl##ed_op#/DIV#ed_cl##ed_op#/SPAN#ed_cl#