Lời giải:
a.
$x^2+6x-7=(x^2-x)+(7x-7)=x(x-1)+7(x-1)=(x-1)(x+7)$
b.
$3x^2+7x-10=(3x^2-3)+(7x-7)=3(x^2-1)+7(x-1)$
$=3(x-1)(x+1)+7(x-1)=(x-1)(3x+3+7)=(x-1)(3x+10)$
c.
$2x(x-1)-(1-x)=2x(x-1)+(x-1)=(x-1)(2x+1)$
d.
$7x(x-y)+2(y-x)^2=7x(x-y)+2(x-y)^2=(x-y)[7x+2(x-y)]=(x-y)(2x+5y)$
e.
$(x-y)^3-x^3+y^3=(x-y)^3-(x-y)(x^2+xy+y^2)$
$=(x-y)[(x-y)^2-(x^2+xy+y^2)]=(x-y)(-3xy)=-3xy(x-y)$
f.
$x^3+5x^2-2x-4$
$=(x^3-x^2)+(6x^2-6x)+(4x-4)$
$=x^2(x-1)+6x(x-1)+4(x-1)=(x-1)(x^2+6x+4)$