Question

数学因式分解题求解

Answer 1

①6x^4+7x^3-36x^2-7x+6
=6(x^2-1)^2+7x(x^2-1)-24x^2
=[2(x^2-1)-3x][3(x^2-1)+8x]
=(2x^2-3x-2)(3x^2+8x-3)
=(x-2)(2x+1)(x+3)(3x-1)
②原式=[(x^2+y^2)+xy]^2-4xy(x^2+y^2)
=(x^2+y^2)^2-2xy(x^2+y^2)+(xy)^2
=(x^2+y^2-xy)^2
③原式=[(x+y)-2xy][(x+y)-2]+(xy-1)^2
=(x+y)^2-2(xy+1)(x+y)+4xy+(xy-1)^2
=(x+y)^2-2(xy+1)(x+y)+(xy+1)^2
=[(x+y)-(xy+1)]^2
=[(x-1)(y-1)]^2
④2x^3-5x-3
=(2x^3+2)-5(x+1)
=2(x+1)(x^2-x+1)-5(x+1)
=(x+1)(2x^2-2x-3)

Answer 2

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