x^3—3x^2+x+1怎么样因式分解?(X的立方减3乘X的平方加X加1 怎么样因式分解)
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x^3—3x^2+x+1怎么样因式分解?(X的立方减3乘X的平方加X加1 怎么样因式分解)
x^3—3x^2+x+1怎么样因式分解?
(X的立方减3乘X的平方加X加1 怎么样因式分解)
x^3—3x^2+x+1怎么样因式分解?(X的立方减3乘X的平方加X加1 怎么样因式分解)
x^3—3x^2+x+1怎么样因式分解?
解法一:
因为x^3—3x^2+x+1
当x=1时,x^3—3x^2+x+1=0
所以有(x-1)因子 .
于是可拆项
x^3—3x^2+x+1=x^3—x^2-2x^2+2x-x+1
=x^2(x-1)-2x(x-1)-(x-1)
=(x-1)(x^2-2x-1)
有理数范围结束
实数范围接下
=(x-1)[(x-1)^2-2]
=(x-1)(x-1+√2)(x-1-√2)
x^3—3x^2+x+1
x=1时,x^3—3x^2+x+1=0
所以有(x-1)因子
x^3—3x^2+x+1
=(x-1)(x^2-2x-1)
x^3—3x^2+x+1
= x^3 - x^2 -x^2 + x - x^2 + 1
= x^2 *(x-1) - x *(x-1) - (x^2 - 1)
= x^2 *(x-1) - x *(x-1) - (x+1)*(x-1)
=(x-1)*(x^2 -x-x-1)
=(x-1)*(x^2 -2x-1)
1
x^3—3x^2+x+1=x^3-x^2-2x^2+2x-x+1
=x^2(x-1)-2x(x-1)-(x-1)
=(x-1)(x^2-2x-1)
=(x-1)[(x-1)^2-2]
=(x-1)(x-1+√2)(x-1-√2)
= x^3 - x^2 -x^2 + x - x^2 + 1
= x^2 *(x-1) - x *(x-1) - (x^2 - 1)
= x^2 *(x-1) - x *(x-1) - (x+1)*(x-1)
=(x-1)*(x^2 -x-x-1)
=(x-1)*(x^2 -2x-1)
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