Evaluation of f(x)=color(blue)(1)x^4color(blue)(-4)x^3color(blue)(+0)x^2color(blue)(-4)xcolor(blue)(+6)f(x)=1x4−4x3+0x2−4x+6
for f(color(red)(-2))f(−2)
Notice the expansion of the expression to include the implied coefficients of color(blue)(1)1 for x^4x4 and of color(blue)(0)0 for x^2x2
Initial set-up:
{:
(,"|",color(blue)(1),color(blue)(-4),color(blue)(+0),color(blue)(-4),color(blue)(+6),color(white)("XXXXXXXX")"line [1]"),
(,"|",,,,,,color(white)("XXXXXXXX")"line[2]"),
("----",,"----","----","----","----","----",),
(xxcolor(red)((-2)),"|",color(green)(1),,,,,color(white)("XXXXXXXX")"line [3]")
:}
For each column
- Multiply the last number written on line [3] by color(red)((-2)) and write the product on line [2] of the next column
- Add the numbers in lines [1] and [2] of the next column and write the sum in line [3] of that column.
The number written in the last column of line [3] will be the value of f(color(red)(-2))
{:
(,"|",color(blue)(1),color(blue)(-4),color(blue)(+0),color(blue)(-4),color(blue)(+6),color(white)("XXXXXXXX")"line [1]"),
(,"|",,-2,12,-24,56,color(white)("XXXXXXXX")"line[2]"),
("-----------",,"----","----","----","----","----",),
(xxcolor(red)((-2)),"|",color(green)(1),-6,12,-28,color(cyan)(62),color(white)("XXXXXXXX")"line [3]")
:}
