CMR: x^4-6x^3+27x^2-54x+32 chia hết cho 2

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CMR: x^4-6x^3+27x^2-54x+32 chia hết cho 2

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aihong 2 tháng 2021-09-27T13:01:32+00:00 1 Answers 19 views 0

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    2021-09-27T13:03:12+00:00

    \[\begin{array}{l}
    {x^4} – 6{x^3} + 27{x^2} – 54x + 32\\
    = {x^4} – {x^3} – 5{x^3} + 5{x^2} + 22{x^2} – 22x – 32x + 32\\
    = {x^3}\left( {x – 1} \right) – 5{x^2}\left( {x – 1} \right) + 22x\left( {x – 1} \right) – 32\left( {x – 1} \right)\\
    = \left( {x – 1} \right)\left( {{x^3} – 5{x^2} + 22x – 32} \right)\\
    = \left( {x – 1} \right)\left( {{x^3} – 2{x^2} – 3{x^2} + 6x + 16x – 32} \right)\\
    = \left( {x – 1} \right)\left[ {{x^2}\left( {x – 2} \right) – 3x\left( {x – 2} \right) + 16\left( {x – 2} \right)} \right]\\
    = \left( {x – 1} \right)\left( {x – 2} \right)\left( {{x^2} – 3x + 16} \right).
    \end{array}\]

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