Question

Divide the polynomial x^3+x^2-2x+3 by (x-1)​

Answer 1

Answer:

x² + 2x + (3 / (x − 1))

Step-by-step explanation:

Start by setting up the division:

.........____________

x − 1 | x³ + x² − 2x + 3

Start with the first term, x³.  Divided by x, that's x².  So:

.........____x²______

x − 1 | x³ + x² − 2x + 3

Multiply x − 1 by x², subtract the result, and drop down the next term:

.........____x²______

x − 1 | x³ + x² − 2x + 3

.........-(x³ − x²)

...........----------

...................2x² − 2x

Repeat the process over again.  First term is 2x².  Divided by x is 2x.  So:

.........____x² + 2x __

x − 1 | x³ + x² − 2x + 3

.........-(x³ − x²)

...........----------

...................2x² − 2x

Multiply, subtract the result, and drop down the next term:

.........____x² + 2x __

x − 1 | x³ + x² − 2x + 3

.........-(x³ − x²)

...........----------

...................2x² − 2x

.................-(2x² − 2x)

.................---------------

.....................................3

x doesn't divide into 3, so that's the remainder.

Therefore, the answer is:

x² + 2x + (3 / (x − 1))