MathJax快速範本-連續綜合除法

 $$ 多項式x^3-8x^2+20x-17\\=a(x-1)(x-2)(x-3)+b(x-1)(x-2)+c(x-1)+d \\ ， 求 a,b,c,d $$

 

$$ 方法一：用f(1),f(2),f(3),f(0)依序算出d,c,b,a $$

 

$$ 方法一：連續綜合除法-本質上和方法一相同 $$

 

 

$$ \begin{gathered}  \left. {\underline {\,  {\begin{array}{*{20}{c}}  1&{ - 8}&{ + 20}&{ - 17} \\   {}&{ + 1}&{ - 7}&{ + 13} \end{array}} \,}}\! \right| \begin{array}{*{20}{c}}  {} \\   { + 1} \end{array} \hfill \\  \left. {\underline {\,  {\begin{array}{*{20}{c}}  1&{ - 7}&{ + 13} \\   {}&{ + 2}&{ - 10} \end{array}} \,}}\! \right| \begin{array}{*{20}{c}}  { - 4} \\   { + 2} \end{array}\begin{array}{*{20}{c}}  { \to d} \\   {} \end{array} \hfill \\  \left. {\underline {\,  {\begin{array}{*{20}{c}}  1&{ - 5} \\   {}&{ + 3} \end{array}} \,}}\! \right| \begin{array}{*{20}{c}}  { + 3} \\   { + 3} \end{array}\begin{array}{*{20}{c}}  { \to c} \\   {} \end{array} \hfill \\  \left. {\underline {\,  1 \,}}\! \right| \begin{array}{*{20}{c}}  { - 2}&{ \to b} \end{array} \hfill \\ \end{gathered} $$