Toán Lớp 8: Làm tính chia:
( $x^{4}$ – 3x ³ + 4x ² – x -3 ) : ( x ² – 2x + 3 )
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Toán Lớp 8: Làm tính chia:
( $x^{4}$ – 3x ³ + 4x ² – x -3 ) : ( x ² – 2x + 3 )
Comments ( 1 )
{x^4} – 3{x^3} + 4{x^2} – x – 3\\
= {x^2}\left( {{x^2} – 2x + 3} \right) – x\left( {{x^2} – 2x + 3} \right) – {x^2} + 2x – 3\\
= {x^2}\left( {{x^2} – 2x + 3} \right) – x\left( {{x^2} – 2x + 3} \right) – \left( {{x^2} – 2x + 3} \right)\\
= \left( {{x^2} – 2x + 3} \right)\left( {{x^2} – x – 1} \right)\\
\Rightarrow {x^4} – 3{x^3} + 4{x^2} – x – 3:\left( {{x^2} – 2x + 3} \right)\\
= {x^2} – x – 1
\end{array}$