How do you divide #(4x^3 - 8x^2 + 7x - 9) ÷ (x + 3)#?

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Answer 1 · 2016-11-23T07:51:10

The quotient is #=(4x^2-20x+67)# and the remainder is #=-210#

You can do a long division

#color(white)(aaaa)##4x^3-8x^2+7x-9##∣##x+3#

#color(white)(aaaa)##4x^3+12x^2##color(white)(aaaaaaa)##∣##4x^2-20x+67#

#color(white)(aaaaaa)##0-20x^2+7x#

#color(white)(aaaaaaaa)##-20x^2-60x#

#color(white)(aaaaaaaaaaa)##+0+67x-9#

#color(white)(aaaaaaaaaaaaaaa)##+67x+201#

#color(white)(aaaaaaaaaaaaaaaaaaa)##0-210#

The quotient is #=(4x^2-20x+67)#

and the remainder is #=-210#

You can get the remainder directly with the remainder theorem

Let #f(x)=4x^3-8x^2+7x-9#

Then, #f(-3)=4*(-3)^3-8(-3)^2+7(-3)-9#

#=-108-72-21-9=-210#

This is the remainder.