餘式定理(1)
Author: 藍邦偉  老師

$ O $

$餘式定理的幾何意義$
$(1)\;除式為一次式$
$ f(x) =(ax-b)Q(x)+r$
$⇒r=f(\;\frac{b}{a}\;)$

$ 請輸入被除式f(x)= $

1

k = 12 (slider from 1 to 16, step 1)
List: {-5, -4, -3, -2, -1, -0.5, -0.25, -0.1, 0.1, 0.25, 0.5, 1, 2, 3, 4, 5}
a = Element(List, k)
b = -2 (slider from -8 to 8, step 1)
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) = x^(3) - 3 * x + 1
g(x) = a * x + b
inputBox1 = Textfield(f)
A = Root(g)
L: x = x(A)
t_A: "$ x=" + (LaTeX[FractionText[x(A)]]) + " $"
B = Intersect(f, L)
t_B: "$y= " + (LaTeX[FractionText[y(B)]]) + " $"
t_L: "$ y=" + (LaTeX[g]) + " $"
text3: "$ r=f(" + (LaTeX[FractionText[x(A)]]) + " )=" + (LaTeX[FractionText[y(B)]]) + "$"
text2: "$ 請拉動滑竿輸入除式：$
$除式為\;" + (LaTeX[If[a ≟ 1, "", If[a ≟ -1, "-"]]]) + "" + (LaTeX[If[abs(a) ≠ 1, FractionText[a]]]) + "x" + (LaTeX[If[b < 0, "-", If[b > 0, "+", ""]]]) + "" + (LaTeX[If[b ≠ 0, abs(b), ""]]) + " $"