(b³-27)/(b-3)=
Write b³ - 27 as b³ + 0b² + 0b - 27
Write this:
b - 3)b³ + 0b² + 0b - 27
b³ divided by b give b²
b²
b - 3)b³ + 0b² + 0b - 27
b² times -3 gives -3b
b²
b - 3)b³ + 0b² + 0b - 27
- 3b²
b² times b gives b³
b²
b - 3)b³ + 0b² + 0b - 27
b³ - 3b²
Draw a line:
b²
b - 3)b³ + 0b² + 0b - 27
b³ - 3b²
Subtract b³ - b³, that gives 0 so we don't write anything
under that. then 0b² minus -3b² is really 0b²+3b² or 3b²
b²
b - 3)b³ + 0b² + 0b - 27
b³ - 3b²
3b²
Bring down the + 0b
b²
b - 3)b³ + 0b² + 0b - 27
b³ - 3b²
3b² + 0b
3b² divided by b give 3b
b² + 3b
b - 3)b³ + 0b² + 0b - 27
b³ - 3b²
3b² + 0b
3b times -3 gives -9b
b² + 3b
b - 3)b³ + 0b² + 0b - 27
b³ - 3b²
3b² + 0b
- 9b
3b times b gives 3b²
b² + 3b
b - 3)b³ + 0b² + 0b - 27
b³ - 3b²
3b² + 0b
3b² - 9b
Draw a line:
b² + 3b
b - 3)b³ + 0b² + 0b - 27
b³ - 3b²
3b² + 0b
3b² - 9b
Subtract 3b² - 3b², that gives 0 so we don't write anything
under that. then 0b minus -9b is really 0b+9b or 9b
b² + 3b
b - 3)b³ + 0b² + 0b - 27
b³ - 3b²
3b² + 0b
3b² - 9b
9b
Bring down the - 27
b² + 3b
b - 3)b³ + 0b² + 0b - 27
b³ - 3b²
3b² + 0b
3b² - 9b
9b - 27
9b divided by b give 9
b² + 3b + 9
b - 3)b³ + 0b² + 0b - 27
b³ - 3b²
3b² + 0b
3b² - 9b
9b - 27
9 times -3 gives -27
b² + 3b + 9
b - 3)b³ + 0b² + 0b - 27
b³ - 3b²
3b² + 0b
3b² - 9b
9b - 27
- 27
9 times b gives 9b
b² + 3b + 9
b - 3)b³ + 0b² + 0b - 27
b³ - 3b²
3b² + 0b
3b² - 9b
9b - 27
9b - 27
Draw a line:
b² + 3b + 9
b - 3)b³ + 0b² + 0b - 27
b³ - 3b²
3b² + 0b
3b² - 9b
9b - 27
9b - 27
Subtract 9b - 9b, that gives 0 so we don't write anything
under that. then -27 minus -27 is really -27+27 or 0, so
the remainder is 0:
b² + 3b + 9
b - 3)b³ + 0b² + 0b - 27
b³ - 3b²
3b² + 0b
3b² - 9b
9b - 27
9b - 27
0
That's it. The answer, or quotient, is b² + 3b + 9
Edwin
