質問: phân tích thành nhân tử: a) $x^{4}$-5$x^{3}$+2$x^{2}$-$x^{1}$+3 b) $x^{3}$+3$x^{2}$-$x^{1}$-3 c) $x^{3}$+2$x^{2}$+4 $x^{1}$+3 d)6$x^{3}$-17$x^{2}$-26$x^{1}$-3 e) $x^{4}$-3$x^{3}$+6$x^{2}$+13$x^{1}$+3
回答: Giải thích các bước giải: $\begin{array}{l} a){x^4} – 5{x^3} + 2{x^2} – x + 3\\ = \left( {{x^4} – {x^3}} \right) – \left( {4{x^3} – 4{x^2}} \right) – \left( {2{x^2} – 2x} \right) – \left( {3x – 3} \right)\\ = \left( {x – 1} \right)\left( {{x^3} – 4{x^2} – 2x – 3} \right)\\ b){x^3} + 3{x^2} – x – 3\\ = \left( {{x^3} + 3{x^2}} \right) – \left( {x + 3} \right)\\ = \left( {x + 3} \right)\left( {{x^2} – 1} \right)\\ = \left( {x + 3} \right)\left( {x – 1} \right)\left( {x + 1} \right)\\ c){x^3} + 2{x^2} + 4x + 3\\ = \left( {{x^3} + {x^2}} \right) + \left( {{x^2} + x} \right) + \left( {3x + 3} \right)\\ = \left( {x + 1} \right)\left( {{x^2} + x + 3} \right)\\ d)6{x^3} – 17{x^2} – 26x – 3\\ = \left( {6{x^3} + 6{x^2}} \right) – \left( {23{x^2} + 23x} \right) – \left( {3x + 3} \right)\\ = \left( {x + 1} \right)\left( {6{x^2} – 23x – 3} \right)\\ e){x^4} – 3{x^3} + 6{x^2} + 13x + 3\\ = \left( {{x^4} + {x^3}} \right) – \left( {4{x^3} + 4{x^2}} \right) + \left( {10{x^2} + 10x} \right) + \left( {3x + 3} \right)\\ = \left( {x + 1} \right)\left( {{x^3} – 4{x^2} + 10x + 3} \right) \end{array}$