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用试根法因式分解:①x^4+3x^3-3x^2-11x-6②x^6+2x^5+3x^4+4x^3+3x^2+2x+1

来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/15 03:19:36
用试根法因式分解:①x^4+3x^3-3x^2-11x-6②x^6+2x^5+3x^4+4x^3+3x^2+2x+1
x^4+3x^3-3X^2-11x-6
=x^3(x+3)-(3x^2+11x+6)
=x^3(x+3)-(x+3)*(3x+2)
=(x+3)(x^3-3x-2)
=(x+3)[x^3-x-2(x+1)]
=(x+3)[x(x+1)(x-1)-2(x+1)]
=(x+3)(x+1)(x^2-x-2)
=(x+3)(x-2)(x+1)^2
x^6+2x^5+3x^4+4x^3+3x^2+2x+1
=x^6+x^5+x^5+x^4+2x^4+2x^3+2x^3+2x^2+x^2+x+x+1
=x^5(x+1)+x^4(x+1)+2x^3(x+1)+2x^2(x+1)+x(x+1)+(x+1)
=(x+1)(x^5+x^4+2x^3+2x^2+x+1)
=(x+1)²(x^4+2x²+1)
=(x+1)²(x²+1)²