Question

若x=，则y=2x⁵-4x⁴-x³-6x²-6的值为    ．

Answer

由x=得3=（x-1）2，利用（x-1）2整体代入，提取公因式化简求解．
【解析】
由x=得3=（x-1）2，
∴y=2x5-4x4-x3-6x2-6
=2x3（x2-2x+1）-2x3-x3-6x2-6
=2x3（x-1）2-3x3-6x2-6
=2x3×3-3x3-6x2-6
=3x3-6x2-6
=3x（x2-2x）-6
=3x（x2-2x+1）-3x-6
=3x（x-1）2-3x-6
=3x•3-3x-6
=9x-3x-6
=6x-6
=6（x-1）
=6．