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What is the remainder when (3x^3 - 2x^2 + 4x - 3) is divided by (x^2 + 3x + 3)?

source : socratic.org

What is the remainder when (3x^3 – 2x^2 + 4x – 3) is divided by (x^2 + 3x + 3)?

#3x^3-2x^2+4x-3#

#=3x^3+9x^2+9x-11x^2-33x-33+28x+30#

#=3x(x^2+3x+3)-11(x^2+3x+3)+28x+30#

#=(x^2+3x+3)(3x-11)+28x+30#

Hence

#(3x^3-2x^2+4x-3)/(x^2+3x+3)#

#=((x^2+3x+3)(3x-11)+28x+30)/(x^2+3x+3)#

#=(3x-11)+(28x+30)/(x^2+3x+3)#

So the remainder of division is

#color(red)(28x+30)#

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