Question

x²-4x+2 x²+3x+1 3x²+3x-3 2x²-2x-1/2 把这四道题目 因式分解，全过程

Answer 1

x²-4x+2=(x²-4x+4)-2=(x-2)²-2=(x-2+√2)(x-2-√2)
x²+3x+1=(x²+3x+9/4)-5/4=(x+3/2)²-5/4=(x+3/2+√5/2)(x+3/2-√5/2)
3x²+3x-3=3(x²+x+1/4)-15/4=3(x+1/2)²-15/4=3(x+1/2+√5/2)(x+1/2-√5/2)
2x²-2x-1/2=2(x²-x+1/4)-1=2(x-1/2)²-1=2(x-1/2+√2/2)(x-1/2-√2/2)

Answer 2

x²-4x+2
=x²-4x+4-2
=(x-2)²-2
=(x-2-√2)(x-2+√2)

x²+3x+1
=x²+3x+9/4-9/4+1
=(x+3/2)²-5/4
=(x+3/2-√5/2)(x+3/2+√5/2)

3x²+3x-3
=3(x²+x-1)
=3(x²+x+1/4-1/4-1)
=3[(x+1/2)²-5/4]
=3(x+1/2-√5/2)(x+1/2+√5/2)

2x²-2x-1/2
=1/2(4x²-4x-2)
=1/2(4x²-4x+1-1-2)
=1/2[(2x-1)²-3]
=1/2(2x-1-√3)(2x-1+√3)