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Mathematics

Divide:

16 + 8x + x6 - 8x3 - 2x4 + x2 by x + 4 - x3

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Dividing 16 + 8x + x6 - 8x3 - 2x4 + x2 by x + 4 - x3

⇒ Dividing x6 - 2x4 - 8x3 + x2 + 8x + 16 by -x3 + x + 4

−x3+x+4)−x3+x+4−x3+x+4)x6−2x4−8x3+x2+8x+16‾−x3+x+4−x6−+2x4−+4x3‾−x3+x+42x3+−x4−4x3+x2+8x+16−x3+x+42x+2−+x4−4x3+−x2+−4x‾−x3+x+42x3++x+−4x3+x2+4x+16−x3+x+42x3++541)−+4x3+x2−+4x+−16‾−x3+x+42x3++5x2+−23x×\begin{array}{l} \phantom{-x^3 + x + 4)}{-x^3 + x + 4} \ -x^3 + x + 4\overline{\smash{\big)}x^6 - 2x^4 - 8x^3 + x^2 + 8x + 16} \ \phantom{-x^3 + x + 4}\underline{\underset{-}{}x^6 \underset{+}{-}\phantom{2}x^4 \underset{+}{-}4x^3} \ \phantom{{-x^3 + x + 4}2x^3+}-x^4 - 4x^3 + x^2 + 8x + 16 \ \phantom{{-x^3 + x + 4}2x+2}\underline{\underset{+}{-}x^4 \phantom{- 4x^3} \underset{-}{+} x^2 \underset{-}{+} 4x} \ \phantom{{-x^3 + x + 4}{2x^3+}{+x+}}-4x^3 \phantom{+ x^2} + 4x + 16 \ \phantom{{-x^3 + x + 4}{2x^3+}{+541)}}\underline{\underset{+}{-}4x^3 \phantom{+ x^2} \underset{+}{-} 4x \underset{-}{+} 16} \ \phantom{{-x^3 + x + 4}{2x^3+}{+5x^2+\qquad}{-23x}}\times \end{array}

Hence, (16 + 8x + x6 - 8x3 - 2x4 + x2) ÷ (x + 4 - x3) = -x3 + x + 4

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