若x=,则y=2x5-4x4-x3-6x2-6的值为________.
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6
解析分析: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.
解答: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.
点评:本题考查因式分解的运用,有公因式时,要先考虑提取公因式;注意运用整体代入法求解.