餘式定理 (2)
Author: 藍邦偉  老師

$ O $

$ 餘式定理的幾何意義\;$
$(2)\;除式為二次式$
$已知f(x)除以(x-a)與(x-b)$
$的餘式分別f(a)與f(b)，\;試求$
$f(x)除以(x-a)(x-b)的餘式$

$ 設f(x)=(x-a)(x-b)Q(x)$
$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;+mx+k $

$ 請輸入二次以上多項式\;f(x)＝ $

1

$ (a,f(a)) $

$ (b,f(b)) $

u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
O = (0, 0)
Q_2: 0.7 * Corner[1] + 0.3 * Corner[2]
Q_3: (x(Q_2), y(Corner[4]))
poly1, q_1, q_2, q_4, q_3 = Polygon(Corner[1], Q_2, Q_3, Corner[4])
f(x) = 0.5 * x^(3) - 2 * x^(2) + 4
inputBox1 = Textfield(f)
C = (-0.29228861191640504, 0.17544424006780004)
D = (4.597201685491182, -0.014673379748172333)
A = DynamicCoordinates(C, floor(x(C)), 0)
B = DynamicCoordinates(D, floor(x(D)), 0)
a: x(A)
b: x(B)
L_1: x = x(A)
L_2: x = x(B)
E = Intersect(f, L_1)
F = Intersect(f, L_2)
t_{Q}: "$ 除式為(x" + (LaTeX[If[a > 0, "-", If[a < 0, "+", ""]]]) + "" + (LaTeX[If[a ≠ 0, abs(a), ""]]) + ")(x" + (LaTeX[If[b > 0, "-", If[b < 0, "+", ""]]]) + "" + (LaTeX[If[b ≠ 0, abs(b), ""]]) + ") $"
L_3 = Line(E, F)
G = Intersect(L_3, yAxis)
k: y(G)
t_{r(x)}: "$ 餘式\;r(x)=mx+k$
$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;= " + (LaTeX[FractionText[Slope[L_3]]]) + "\;x" + (LaTeX[If[k > 0, "+", If[k < 0, "-", ""]]]) + "" + (LaTeX[If[k ≠ 0, abs(k), ""]]) + "$
$即通過(a,f(a)),(b,f(b))的直線$"
t_L: "$ y=" + (LaTeX[FractionText[Slope[L_3]]]) + "\;x" + (LaTeX[If[k > 0, "+", If[k < 0, "-", ""]]]) + "" + (LaTeX[If[k ≠ 0, abs(k), ""]]) + "$"