多項式(20)
Author: 藍邦偉　老師

$ (1) 正確,f(x)的次數可能是二次以上$

$ (2)設A(-3,-1),B(0,5),C(1,7)⇒m_{\overline{AB} }=\frac{5-(-1)}{0-(-3)}=2=\frac{7-5}{1-0}=m_{\overline{BC}}$

$ (3) 除式三次式,餘式至多二次式 $

$∴A,B,C共線⇒f(x)=2x+5,故此選項錯誤 $

$ (5)f(x)=ax(x-1)+bx+5 $

$ ⇒f(1)=b+5=7⇒b=2 $

⇒f(-3)=a(-3)(-4)+2(-2)+5=-1

$ ⇒a=\frac{1}{6} $

$ ⇒f(x)=\frac{1}{6} x(x-1)+2x+5$

$ ⇒f(-2)=\frac{1}{6}(-2)(-3)+2(-2)+5=2 $

$ (4)餘式應為(-1)×\frac{x(x-1)}{(-3-0)(-3-1)}+5×\frac{(x+3)(x-1)}{(0+3)(0-1)}+7×\frac{x(x+3)}{(1-0)(1+3)} $

n = 6 (slider from 0 to 12, step 1)
A = (-4.384945092682924, 0.995788507317074)
B: A + (2.2, 0)
D: A + (0, 0.9)
C: B + D - A
poly1, a, b, c, d = Polygon(A, B, C, D)