Question

How do you long divide `2x^3- 3x^2+ 3x - 4` by `x-2`?

Answer 1

`(2x^3-3x^2+3x-4) div (x-2) = (2x^2 - x + 1) R:(-2)`

Explanation:

`color(red)("[A]")` `x` (the leading term of `(x-2)` goes into `2x^3` (the leading term of `(2x^3-3x^2+3x-4)`, `(2x^2)` times.

`color(red)("[B]")`Multiply `(x-2)` by `(2x^2)` and subtract from the dividend.

`color(red)("[C]")`"Bring down" the next term (`3x`); the first term of `(x-2)` goes into `(-x^2+3x)`, `(-x)` times.

`color(red)("[D]")`Multiply `(x-2)` by `(-x)` and subtract.

`color(red)("[E]")`"Bring down" the final term (`-4`); divide the first term of `(x-2)` (that is, `x`) into `(1x-4)` giving `1`; multiply `(x-2)` by `(1)`; and subtract giving the remainder.