Question

Descompuneti in factori ireductibili:
(x^2+x+1)(x^2+x+2)-12=?
(x+1)(x+3)(x+5)(x+7) +15=?
X^4-Y^4-a^4-4ax^2y+2a^2y^2= ?

Answer 1

(x²+x+1)(x²+x+2)-12 =
= x^4+x³+2x²+x³+x²+2x+x²+x+2-12 = 
= x^4+2x³+4x²+3x-10

(x+1)(x+3)(x+5)(x+7) +15=
= (x²+3x+x+3)(x+5)(x+7) +15 =
= (x²+4x+3)(x+5)(x+7)+15 = 
= (x³+5x²+4x²+20x+3x+15)(x+7)+15 = 
= (x³+9x²+23x+15)(x+7)+15 =
= x^4+7x³+9x³+63x²+23x²+161x+15x+105+15 =
= x^4+16x³+86x²+176x+120