a. x3 – 3x2 – 4x + 12
= (x3 – 3x2 ) – (4x – 12)
= x2(x – 3) – 4(x – 3)
= (x – 3)(x2 – 4)
= (x – 3)(x + 2)(x – 2)
b. x4 – 5x2 + 4
= x4 – 4x2 - x2 + 4
= (x4 – 4x2 ) – (x2 - 4)
= x2(x2 – 4) – (x2 – 4)
= (x2 – 4)( x2 – 1)
= (x + 2)(x – 2)(x + 1)(x – 1)
c. (x + y + z)3 – x3 – y3 – z3
= [(x + y) + z]3 – x3 – y3 – z3
= (x + y)3 + 3(x + y)2z + 3(x + y)z2 + z3 – x3 – y3 – z3
= x3 + y3 + 3xy(x + y) + 3(x + y)2z + 3(x + y)z2 – x3 – y3
( vì z3 – z3 = 0 ; 3x2y + 3xy2 = 3xy (x + y) ).
= 3xy.(x+ y) + 3( x+ y)2.z + 3(x+ y).z2
= 3(x + y)[xy + (x + y)z + z2]
= 3(x + y)[xy + xz + yz + z2]
= 3(x + y)[x(y + z) + z(y + z)]
= 3(x + y)(y + z)(x + z)
