Question

What is `x^3-2x^2+4x-3` divided by x-1?

Answer 1

`x^2-x+3`

Explanation:

Factor by grouping, splitting each term so that the binomials are each divisible by `(x-1)`:

`x^3-2x^2+4x-3 = (x^3-x^2)-(x^2-x)+(3x-3)`

`color(white)(x^3-2x^2+4x-3) = x^2(x-1)-x(x-1)+3(x-1)`

`color(white)(x^3-2x^2+4x-3) = (x^2-x+3)(x-1)`

So:

`(x^3-2x^2+4x-3)/(x-1) = x^2-x+3`

`color(white)()`
Alternatively, you can long divide the coefficients like this:

The dividend `x^3-2x^2+4x-3` is represented by the the sequence `1, -2, 4, 3`, the divisor `x-1` by the sequence `1, -1` and the resulting quotient is `1, -1, 3` representing `x^2-x+3`