分解因式 求大神 5
3个回答
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2x^4-15x^3+38x^2-39x+14
=(2x^4-2x^3)-(13x^3-13x^2)+(25x^2-25x)-(14x-14)
=2x^3(x-1)-13x^2(x-1)+25x(x-1)-14(x-1)
=(x-1)(2x^3-13x^2+25x-14)
=(x-1)[(2x^3-2x^2)-(11x^2-11x)+(14x-14)]
=(x-1)[2x^2(x-1)-11x(x-1)+14(x-1)]
=(x-1)^2(2x^2-11x+14)
=(x-1)^2[(2x^2-4x)-(7x-14)]
=(x-1)^2[2x(x-2)-7(x-2)]
=(x-1)^2(x-2)(2x-7)
=(2x^4-2x^3)-(13x^3-13x^2)+(25x^2-25x)-(14x-14)
=2x^3(x-1)-13x^2(x-1)+25x(x-1)-14(x-1)
=(x-1)(2x^3-13x^2+25x-14)
=(x-1)[(2x^3-2x^2)-(11x^2-11x)+(14x-14)]
=(x-1)[2x^2(x-1)-11x(x-1)+14(x-1)]
=(x-1)^2(2x^2-11x+14)
=(x-1)^2[(2x^2-4x)-(7x-14)]
=(x-1)^2[2x(x-2)-7(x-2)]
=(x-1)^2(x-2)(2x-7)
追问
矮油'好快啊
追答
老实说,复制的
其实,做这种题用的就是
双十字相乘法,或者是多十字相乘法
画图其实更容易理解
例子 例:3x^2;+5xy-2y^2;+x+9y-4=(x+2y-1)(3x-y+4)
因为3=1×3,-2=2×(-1),-4=(-1)×4,双十字相乘法
而1×(-1)+3×2=5,2×4+(-1)(-1)=9,1×4+3×(-1)=1
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