作业帮1.计算(x+1)(x²+1)(x^4+1)(x^8+1)(x^16+1)
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/21 22:12:13
1.计算(x+1)(x²+1)(x^4+1)(x^8+1)(x^16+1)
2.p.m为何值时,x³+px-2能被x²+mx-1整除
2.p.m为何值时,x³+px-2能被x²+mx-1整除
原式=(x+1)(x^2+1)(x^4+1)(x^8+1)(x^16+1)(x-1)/(x-1)
=(x^2-1)(x^2+1)(x^4+1)(x^8+1)(x^16+1)/(x-1)
=(x^4-1)(x^4+1)(x^8+1)(x^16+1)/(x-1)=(x^8-1)(x^8+1)(x^16+1)/(x-1)
=(x^16-1)(x^16+1)/(x-1)=(x^32-1)/(x-1)
x^3+px-2=x^3+mx^2-x-mx^2+(p+1)x-2=x(x^2+mx-1)+(-mx^2+(p+1)x-2)
所以,-mx^2+(p+1)x-2=k(x^2+mx-1)
-2=k*(-1) , k=2, m=-2, p+1=-4, p=-5
所以,m=-2,p=-5
=(x^2-1)(x^2+1)(x^4+1)(x^8+1)(x^16+1)/(x-1)
=(x^4-1)(x^4+1)(x^8+1)(x^16+1)/(x-1)=(x^8-1)(x^8+1)(x^16+1)/(x-1)
=(x^16-1)(x^16+1)/(x-1)=(x^32-1)/(x-1)
x^3+px-2=x^3+mx^2-x-mx^2+(p+1)x-2=x(x^2+mx-1)+(-mx^2+(p+1)x-2)
所以,-mx^2+(p+1)x-2=k(x^2+mx-1)
-2=k*(-1) , k=2, m=-2, p+1=-4, p=-5
所以,m=-2,p=-5
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