Find the quotient and remainder when x4 + 2x3 + 3x2 + 4x + 5 / (x – 1) (x – 2)

Find the quotient and remainder when
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1 Answer

(x-1)(x-2)=x2-3x+2.

Algebraic long division:

                x2+5x  +16              quotient

x2-3x+2 ) x4+2x3 +3x2  +4x+5

               x4 -3x3  +2x2

                    5x3    +x2  +4x

                    5x3-15x2+10x

                          16x2  -6x  +5

                          16x2-48x+32

                                   42x-27 remainder

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