phân tích đa thức thành nhân tử (8x-4x^2-1)(x^2+2x+1)-4(x^2+x+1) 17/07/2021 Bởi Reese phân tích đa thức thành nhân tử (8x-4x^2-1)(x^2+2x+1)-4(x^2+x+1)
Đáp án: \({\left( {x – 1} \right)^2}\left( { – 4{x^2} – 8x – 5} \right)\) Giải thích các bước giải: \(\begin{array}{l}(8x – 4{x^2} – 1)({x^2} + 2x + 1) – 4({x^2} + x + 1)\\ = 8{x^3} + 16{x^2} + 8x – 4{x^4} – 8{x^3} – 4{x^2} – {x^2} – 2x – 1 – 4{x^2} – 4x – 4\\ = – 4{x^4} + 7{x^2} + 2x – 5\\ = – 4{x^4} + 4{x^3} – 4{x^3} + 4{x^2} + 3{x^2} – 3x + 5x – 5\\ = – 4{x^3}\left( {x – 1} \right) – 4{x^2}\left( {x – 1} \right) + 3x\left( {x – 1} \right) + 5\left( {x – 1} \right)\\ = \left( {x – 1} \right)\left( { – 4{x^3} – 4{x^2} + 3x + 5} \right)\\ = \left( {x – 1} \right)\left( { – 4{x^3} + 4{x^2} – 8{x^2} + 8x – 5x + 5} \right)\\ = \left( {x – 1} \right)\left[ { – 4{x^2}\left( {x – 1} \right) – 8x\left( {x – 1} \right) – 5\left( {x – 1} \right)} \right]\\ = {\left( {x – 1} \right)^2}\left( { – 4{x^2} – 8x – 5} \right)\end{array}\) Bình luận
Đáp án:
\({\left( {x – 1} \right)^2}\left( { – 4{x^2} – 8x – 5} \right)\)
Giải thích các bước giải:
\(\begin{array}{l}
(8x – 4{x^2} – 1)({x^2} + 2x + 1) – 4({x^2} + x + 1)\\
= 8{x^3} + 16{x^2} + 8x – 4{x^4} – 8{x^3} – 4{x^2} – {x^2} – 2x – 1 – 4{x^2} – 4x – 4\\
= – 4{x^4} + 7{x^2} + 2x – 5\\
= – 4{x^4} + 4{x^3} – 4{x^3} + 4{x^2} + 3{x^2} – 3x + 5x – 5\\
= – 4{x^3}\left( {x – 1} \right) – 4{x^2}\left( {x – 1} \right) + 3x\left( {x – 1} \right) + 5\left( {x – 1} \right)\\
= \left( {x – 1} \right)\left( { – 4{x^3} – 4{x^2} + 3x + 5} \right)\\
= \left( {x – 1} \right)\left( { – 4{x^3} + 4{x^2} – 8{x^2} + 8x – 5x + 5} \right)\\
= \left( {x – 1} \right)\left[ { – 4{x^2}\left( {x – 1} \right) – 8x\left( {x – 1} \right) – 5\left( {x – 1} \right)} \right]\\
= {\left( {x – 1} \right)^2}\left( { – 4{x^2} – 8x – 5} \right)
\end{array}\)