Question

Descompuneti in factori(rezolvarea pas cu pas):
a)x³-6x²+11x-6
b)x³-3x+2
c)x³-x-6
d) x^4+x³+x²+3x+2
e) x^4 +4
f) x^4+2x²+9
g) x^4+4y^4
h) a^4-2a³+2a²-2a+1
i) a^4+4a³+8a²+16a+16
j)(x²+2x)(x²+2x+3)+2
k)(x²+2x+4)²-5( x^4+4x²+16)+(2x²-4x+8)²

Answer 1

a) x³-3x²-3x²+9x+2x-6 = x²(x-3) -3x(x-3)+2 (x-3)=
     = (x-3)*(x²-3x+2) = (x-3)*(x-2)*(x-1)
     x²-3x+2 = x²-2x-x+2 = x(x-2) -(x-2)= (x-2)*(x-1)
b)x³-4x+x+2= x(x²-4)+ (x+2) = x(x-2)(x+2) + (x+2) = (x+2) [x(x-2) +1]=
  = (x+2)*(x²-2x+1)= (x+2) * (x-1)²
c) x³-4x+3x-6 = x(x²-4) +3(x-2) = x(x-2)(x+2)+ 3(x-2)= (x-2) [x(x+2)+3] = 
   = (x-2) (x²+2x+3)
e) (x^4 + 4x^2 + 4) - 4x^2
= (x^2 + 2)^2 - (2x)^2 
= (x^2 + 2 + 2x)(x^2 + 2 - 2x)
= (x^2 + 2x + 2)(x^2 - 2x + 2). 
f)x^4 + 2x^2 + 9 
= (x^2 - 2x +3)(x^2 + 2x + 3)
g) x4 + 4y4 = 0
x4 + 4y4 + -4y4 = 0 + -4y4
4y4 + -4y4 = 0
x4 + 0 = 0 + -4y4
x4 = 0 + -4y4
x4 = -4y4
-4y4 + 4y4 = 0
x4 + 4y4 = 0
Doar aceste subpuncte mi.au dat corect.