Question

HELP!! :>
Descompuneți in factori:

a) (x+1)³-4(x+1)
b) (x-5)³-(x+5)
c) (x-1)³-9(x-1)
d) (x+2)³-25(x+2)
e) (x-3)³-49(x-3)
f) (2x+1)³-16(2x+1)

Answer 1

a) (x+1)^3-4(x+1)=
=(x+1)[(x+1)^2-2^2]=
=(x+1)[(x+1)-2][(x+1)+2]=
=(x+1)(x-1)(x+3)

b) (x-5)^3-(x-5)=
=(x-5)[(x-5)^2-1^2]=
=(x-5)[(x-5)-1][(x-5)+1]=
=(x-5)(x-6)(x-4)

b') (x+5)^3-(x+5)=
=(x+5)[(x+5)-1][(x+5)+1]=
=(x+5)(x+4)(x+6)

c) (x-1)^3-9(x-1)=
=(x-1)[(x-1)^2-3^2]=
=(x-1)[(x-1)-3][(x-1)+3]=
=(x-1)(x-4)(x+2)

d) (x+2)^3-25(x+2)=
=(x+2)[(x+2)^2-5^2]=
=(x+2)(x+2-5)(x+2+5)=
=(x+2)(x-3)(x+7)

e) (x-3)^3-49(x-3)=
=(x-3)[(x-3)^2-7^2]=
=(x-3)(x-3-7)(x-3+7)=
=(x-3)(x-10)(x+4)

f) (2x+1)^3-16(2x+1)=
=(2x+1)[(2x+1)^2-4^2]=
=(2x+1)(2x+1-4)(2x+1+4)=
=(2x+1)(2x-3)(2x+5)