Question

因式分解 x^4+2x^3+6x^2+4x+8; x^4-3x+1; x^2y^2-4xy-x^2-y^2+1

Answer 1

额。。。因式分解，要都化成乘积的形式。²
第一题：
x^4+2x^3+6x^2+4x+8
=x^4+6x^2+8+2x^3+4x
=(x^2+2)(x^2+4)+2x(x^2+2)
=(x^2+2)(x^2+4+2x)

第三题：
x^2y^2-4xy-x^2-y^2+1
=x^2y^2-2xy+1-x^2-y^2- 2xy
=(xy-1)^2 - (x+y)^2
=(xy-1+x+y)(xy-1-x-y)

Answer 2

x^4+2x^3+6x^2+4x+8 = x^3(x+2)+4(x+2)+6x^2 = (x^3+4)(x+2)+6x^2
x^4-3x+1 = x(x^3-3)+1
x^2y^2-4xy-x^2-y^2+1 = x^2y^2 - 2xy- (2xy+x^2+y^2)+1 = (xy-1)^2 - (x+y)^2

Answer 3

x^4+2x^3+6x^2+4x+8 = x^3(x+2)+4(x+2)+6x^2 = (x^3+4)(x+2)+6x^2x^4-3x+1 = x(x^3-3)+1