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

1 Answer
Jan 8, 2017

#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:

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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#