Question

用秦九韶算法求多项式f（x）=x5+5x4+10x3+10x2+5x+1，当x=-2时的值是______

用秦九韶算法求多项式f（x）=x5+5x4+10x3+10x2+5x+1，当x=-2时的值是______．

Answer 1

f（x）=x⁵+5x⁴+10x³+10x²+5x+1
=（x⁴+5x³+10x²+10x+5）x+1
=[（x³+5x²+10x+10）x+5]x+1
={{[（x+5）x+10]x+10}x+5}x+1
∴在x=-2时的值时的值为{{[（x+5）x+10]x+10}x+5}x+1
={{[（-2+5）（-2）+10]（-2）+10}（-2）+5}（-2）+1=-1
故答案为：-1．