How do you simplify and divide #(x^3-4x^2+5x-6)/(x^2-x+2)#? Precalculus Real Zeros of Polynomials Long Division of Polynomials 1 Answer Binayaka C. Jul 24, 2017 # (x-3)# Explanation: # (x^3 -4x^2 +5x -6 )/(x^2-x+2) # # = (x^3- 3x^2 -x^2+3x +2x -6 )/(x^2-x+2) # #= (x^2(x- 3) -x(x-3) +2(x -3 ))/(x^2-x+2) # #= ((x- 3) cancel((x^2-x+2)))/cancel((x^2-x+2) ) # #= (x-3)# [Ans] Answer link Related questions What is long division of polynomials? How do I find a quotient using long division of polynomials? What are some examples of long division with polynomials? How do I divide polynomials by using long division? How do I use long division to simplify #(2x^3+4x^2-5)/(x+3)#? How do I use long division to simplify #(x^3-4x^2+2x+5)/(x-2)#? How do I use long division to simplify #(2x^3-4x+7x^2+7)/(x^2+2x-1)#? How do I use long division to simplify #(4x^3-2x^2-3)/(2x^2-1)#? How do I use long division to simplify #(3x^3+4x+11)/(x^2-3x+2)#? How do I use long division to simplify #(12x^3-11x^2+9x+18)/(4x+3)#? See all questions in Long Division of Polynomials Impact of this question 2757 views around the world You can reuse this answer Creative Commons License