Problem:  Divide
 x4 - 2x3 + 8x - 14x2 - 3

Set up the long division.
Notice the 0's put in as place
holders for missing powers of x.
 x2 = x4x2 .
Choose x2 since
x2 · x2 matches x4.
x4 + 0x3- 3x2 = x2(x2 + 0x - 3).
Subtract x4 + 0x3 - 3x2 from
x4 - 2x3 + 0x2 + 8x - 14.
Result is -2x3 + 3x2 + 8x - 14.
 -2x = -2x3x2 .
Choose -2x since
-2x · x2 matches -2x3.
-2x3 + 0x2 + 6x = -2x(x2 + 0x - 3).
Subtract -2x3 + 0x2 + 6x from
-2x3 + 3x2 + 8x - 14..
Result is 3x2 + 2x - 14.
 3 = 3x2x2 .
Choose 3 since
3 · x2 matches 3x2.
3x2 + 0x2 - 9 = 3(x2 + 0x - 3).
Subtract 3x2 + 0x2 - 9 from
3x2 + 2x - 14..
Result is 2x - 5.
2x - 5 is the remainder.

 Answer: x4 - 2x3 + 8x - 14x2 - 3 = x2 - 2x + 3 + 2x - 5x2 - 3 .
Notes
x4 - 2x3 + 8x - 14 = (x2 - 3)(x2 - 2x + 3) + 2x - 5
Dividend x4 - 2x3 + 8x - 14
Divisor x2 - 3
Quotient x2 - 2x + 3
Remainder 2x - 5
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}