a. x^4 - 2x^3 + x^2
= x^2 (x^2 - 2x + 1)
= x^2 (x-1)^2
b. x^3 - x + 3x^2y + 3xy^2 + y^3 - y
= x^3 + 3x^2y + 3xy^2 + y^3 - (x+y)
= (x + y)^3 - (x+y)
= (x + y)[(x+y)^2-1]
= (x + y)(x + y - 1)(x + y + 1)
c. 5x^2 - 20z^2 + 5y^2 - 20xy
= 5(x^2 - 4z^2 + y^2 - 4xy)
= 5[x^2 - 2xy + y^2 - 4z^2 - 2xy]
= 5[(x-y)^2 -(2z)^2 - 2xy]
= 5[(x - y -2z)(x - y + 2z) - 2xy
d. x^2 + 5x - 6
= x(x - 1) + 6(x - 1)
= (x + 6)(x - 1)
e. -6x^2 + 7x -2
= -6x(x - 1/2) + 4(x-1/2)
= (4 - 6x)(x - 1/2)
g.-5x^2 + 16x -3
= -5x(x-3) + (x - 3)
= (1 - 5x)(x - 3)
