搜搜做题作业网因式分解 x^4-4x^3+4x^2-9
来源：学生作业帮 编辑：搜搜做题作业网作业帮 分类：数学作业 时间：2024/08/06 20:22:51
因式分解 x^4-4x^3+4x^2-9
x^4-4x^3+4x^2-9
=x^4-3x³-x³+3x²+x²-9
=x³(x-3)-x²(x-3)+(x+3)(x-3)
=(x-3)(x³-x²+x+3)
=(x-3)[(x³+x²)-(2x²-x-3)]
=(x-3)[x²(x+1)-(x+1)(2x-3)]
=(x-3)(x+1)(x²-2x+3)
=x^4-3x³-x³+3x²+x²-9
=x³(x-3)-x²(x-3)+(x+3)(x-3)
=(x-3)(x³-x²+x+3)
=(x-3)[(x³+x²)-(2x²-x-3)]
=(x-3)[x²(x+1)-(x+1)(2x-3)]
=(x-3)(x+1)(x²-2x+3)