Question

若x=，則y=2x⁵-4x⁴-x³-6x²-6的值為    ．

Answer 1

【答案】分析：由x=得3=（x-1）²，利用（x-1）²整體代入，提取公因式化簡求解．
解答：解：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．
點評：本題考查因式分解的運用，有公因式時，要先考慮提取公因式；注意運用整體代入法求解．