(1)
令3x^2-10x+7=0,△=10^2-4×3×7=16
则x=(10±4)/6
x=7/3或x=1
所以3x^2-10x+7=3(x-7/3)(x-1）=(3x-7)(x-1)
(2)
4x^2+8x-21=0,△=8^2-4×4×(-21)=400
则x=(-8±20)/8
x=-7/2或x=3/2
4x^2+8x-21=4(x+7/2)(x-3/2)=(2x+7)(2x-3)
(3)
3x^2+4xy-y^2
=3(x^2+(4/3)xy+(4/9)y^2)-(4/3)y^2-y^2
=3(x+(2/3)y)^2-(7/3)y^2
=3[(x+(2/3)y)^2-(7/9)y^2]
=3(x+(2/3)y+(√7/3)y)(x+(2/3)y-(√7/3)y)
=3(x+((2+√7)/3)y)(x+((2-√7)/3)y)