Question

Descompuneti urmatoarele expresii in produs de factori primi ireductibili:
a) 3x la a 3 +6x la a2 +3x= b) 4x(x+1)-3(x-1)= c) (x+1)la a 2-9=
d)4x la a 2 -(x-1) la a 2= e) xla 2 +6x +8= f) x la a 2 -9x+14=
g)x la a 3 + 3x la a 2 - 4x - 12= h) xla a 3 + 2x la a2 -9x-18= i)x la a 2 -6x-16=

Answer 1

a) 3x³ +6x² +3x =3x(x²+2x +1) = 3x(x+1)²
c) (x+1)² -9 = (x+1+3)(x+1-3) = (x+4)(x-2)
d) 4x² -(x-1)² = (2x+x-1)(2x-x+1)=(3x-1)(x+1)
e) x² +6x +8 = x² +4x +2x + 8 = x(x+4) +2(x+4) = (x+4)(x+2)
f) x² -9x +14 = x² -7x -2x +14 = x(x-2) -7(x-2) = (x-2)(x-7)
g) x³ +3x² -4x -12 = x²(x+3) -4(x+3)=(x+3)(x²-4) = (x+3)(x+2)(x-2)
h) x³ +2x² -9x -18 = x²(x+2) -9(x+2) = (x+2)(x²-9) = (x+2)(x+3)(x-3)
i) x² -6x -16 = x² -8x +2x -16 = x(x+2) -8(x+2) = (x+2)(x-8)