You could do this by long division.
x^2
x - 3)x^3 - 5x^2 + 3x - 8 The first term is x^3, so put x^2 on the top and multiply (x - 3) by the x^2.
x^3 - 3x^2 ------- now subtract this, x^3 - 3x^2 from the x^3 - 5x^2 above it, to give,
x^2
x - 3)x^3 - 5x^2 + 3x - 8
x^3 - 3x^2
- 2x^2 - this is the result of the subtraction, now bring down the next term, + 3x giving
x^2
x - 3)x^3 - 5x^2 + 3x - 8
x^3 - 3x^2
- 2x^2 + 3x The first term here is -2x^2, so put -2x on the top and multiply (x - 3) by the -2x.
x^2 - 2x
x - 3)x^3 - 5x^2 + 3x - 8
x^3 - 3x^2
- 2x^2 + 3x.
- 2x^2 + 6x ---- now subtract this, - 2x^2 + 6x from the - 2x^2 + 3x above it, to give,
x^2 - 2x
x - 3)x^3 - 5x^2 + 3x - 8
x^3 - 3x^2
- 2x^2 + 3x
- 2x^2 + 6x
- 3x --- this is the result of the subtraction, now bring down the next term, - 8 giving
x^2 - 2x
x - 3)x^3 - 5x^2 + 3x - 8
x^3 - 3x^2
- 2x^2 + 3x
- 2x^2 + 6x
- 3x - 8 The first term here is -3x, so put -3 on the top and multiply (x - 3) by the -3.
x^2 - 2x – 3
x - 3)x^3 - 5x^2 + 3x - 8
x^3 - 3x^2
- 2x^2 + 3x
- 2x^2 + 6x
- 3x – 8
-3x + 9 ----- now subtract -3x – 9 from the -3x – 8 above
x^2 - 2x – 3
x - 3)x^3 - 5x^2 + 3x - 8
x^3 - 3x^2
- 2x^2 + 3x
- 2x^2 + 6x
- 3x – 8
- 3x + 9
-17 ---- this is the remainder
Result of the division of x^3 - 5x^2 + 3x – 8 by (x – 3) is,
Quotient = x^2 - 2x – 3, Remainder = -17