What is x^3-2x^2+4x-3x3−2x2+4x−3 divided by x-1?

1 Answer
George C.
Jan 8, 2017

x^2-x+3x2−x+3

Explanation:

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

x^3-2x^2+4x-3 = (x^3-x^2)-(x^2-x)+(3x-3)x3−2x2+4x−3=(x3−x2)−(x2−x)+(3x−3)

color(white)(x^3-2x^2+4x-3) = x^2(x-1)-x(x-1)+3(x-1)x3−2x2+4x−3=x2(x−1)−x(x−1)+3(x−1)

color(white)(x^3-2x^2+4x-3) = (x^2-x+3)(x-1)x3−2x2+4x−3=(x2−x+3)(x−1)

So:

(x^3-2x^2+4x-3)/(x-1) = x^2-x+3x3−2x2+4x−3x−1=x2−x+3

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

enter image source here

The dividend x^3-2x^2+4x-3x3−2x2+4x−3 is represented by the the sequence 1, -2, 4, 31,−2,4,3, the divisor x-1x−1 by the sequence 1, -11,−1 and the resulting quotient is 1, -1, 31,−1,3 representing x^2-x+3x2−x+3

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