Question

divide the following polynomials.
$(x^{3}-3x^{2}+4x-2)\div(x-1)=$

Explanation:

Step1: Divide leading terms

$\frac{x^3}{x} = x^2$

Step2: Multiply divisor by $x^2$

$x^2(x-1) = x^3 - x^2$

Step3: Subtract from dividend

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

Step4: Divide new leading terms

$\frac{-2x^2}{x} = -2x$

Step5: Multiply divisor by $-2x$

$-2x(x-1) = -2x^2 + 2x$

Step6: Subtract from new dividend

$(-2x^2 + 4x - 2) - (-2x^2 + 2x) = 2x - 2$

Step7: Divide new leading terms

$\frac{2x}{x} = 2$

Step8: Multiply divisor by 2

$2(x-1) = 2x - 2$

Step9: Subtract to find remainder

$(2x - 2) - (2x - 2) = 0$

Answer:

$x^2 - 2x + 2$