Toán Lớp 8: (x^4-3x^3+4x^2-3-x):(x^2-2x+3)
(14x-13x^2-15+6×63):(-X+2X^2+3)
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Toán Lớp 8: (x^4-3x^3+4x^2-3-x):(x^2-2x+3)
(14x-13x^2-15+6×63):(-X+2X^2+3)
Comments ( 2 )
{x^4} – 3{x^3} + 4{x^2} – 3 – x\\
= {x^4} – 2{x^3} + 3{x^2} – {x^3} + 2{x^2} – 3x\\
– {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)\\
\Leftrightarrow \left( {{x^4} – 3{x^3} + 4{x^2} – 3 – x} \right):\left( {{x^2} – 2x + 3} \right)\\
= \left( {{x^2} – 2x + 3} \right)\left( {{x^2} – x – 1} \right):\left( {{x^2} – 2x + 3} \right)\\
= {x^2} – x – 1\\
b)\\
14x – 13{x^2} – 15 + 6{x^3}\\
= 6{x^3} – 13{x^2} + 14x – 15\\
= 6{x^3} – 3{x^2} + 9x – 10{x^2} + 5x – 15\\
= 3x\left( {2{x^2} – x + 3} \right) – 5\left( {2{x^2} – x + 3} \right)\\
= \left( {2{x^2} – x + 3} \right)\left( {3x – 5} \right)\\
\Leftrightarrow \left( {14x – 13{x^2} – 15 + 6{x^3}} \right):\left( { – x + 2{x^2} + 3} \right)\\
= \left( {2{x^2} – x + 3} \right)\left( {3x – 5} \right):\left( {2{x^2} – x + 3} \right)\\
= 3x – 5
\end{array}$