a) ( 2x^4 + x^3 – 5x^2 – 3x -3 ): (x^2 -3) 06/08/2021 Bởi Mackenzie a) ( 2x^4 + x^3 – 5x^2 – 3x -3 ): (x^2 -3)
Đáp án: \(2{x^2} + x + 1\) Giải thích các bước giải: \(\begin{array}{l}\,\,\,\,2{x^4} + {x^3} – 5{x^2} – 3x – 3\\ = 2{x^4} – 6{x^2} + {x^3} – 3x + {x^2} – 3\\ = 2{x^2}\left( {{x^2} – 3} \right) + x\left( {{x^2} – 3} \right) + \left( {{x^2} – 3} \right)\\ = \left( {{x^2} – 3} \right)\left( {2{x^2} + x + 1} \right)\\ \Rightarrow \left( {2{x^4} + {x^3} – 5{x^2} – 3x – 3} \right):\left( {{x^2} – 3} \right)\\\,\, = \left( {{x^2} – 3} \right)\left( {2{x^2} + x + 1} \right):\left( {{x^2} – 3} \right)\\\,\, = 2{x^2} + x + 1\end{array}\) Bình luận
Đáp án:
\(2{x^2} + x + 1\)
Giải thích các bước giải:
\(\begin{array}{l}
\,\,\,\,2{x^4} + {x^3} – 5{x^2} – 3x – 3\\
= 2{x^4} – 6{x^2} + {x^3} – 3x + {x^2} – 3\\
= 2{x^2}\left( {{x^2} – 3} \right) + x\left( {{x^2} – 3} \right) + \left( {{x^2} – 3} \right)\\
= \left( {{x^2} – 3} \right)\left( {2{x^2} + x + 1} \right)\\
\Rightarrow \left( {2{x^4} + {x^3} – 5{x^2} – 3x – 3} \right):\left( {{x^2} – 3} \right)\\
\,\, = \left( {{x^2} – 3} \right)\left( {2{x^2} + x + 1} \right):\left( {{x^2} – 3} \right)\\
\,\, = 2{x^2} + x + 1
\end{array}\)