Question

Descompuneti în factori :

x^3+x^2+4x+4
x^3-x^2+3x-3
x^3+2x^2-9x-18
2x^3+x^2-4x-2
x^5-4x^4-9x-36
1-x+x^2-x^3
2) descompuneti :apare factorul X-a
X^3-3x+2,a=1

Answer 1

x³+x²+4x+4=x²(x+1)+4(x+1)=(x+1)(x²+4)
x³-x²+3x-3=x²(x-1)+3(x-1)-(x-1)(x²+3)
x³+2x²-9x-18=x²(x+2)-9(x+2)=(x+2)(x²-9)=(x+2)(x+3)(x-3)
2x³+x²-4x-2=x²(2x+1)-2(2x+1)=(x²-2)(2x+1)
x⁵-4x⁴-9x-36=x⁴(x-4)-9(x-4)=(x-4)(x⁴-9)=(x-4)(x²-3)(x²+3)
1-x+x²-x³=(1-x)+x²(1-x)=(1-x)(1+x²)

x³-3x+2=x³-x-2x+2=x(x²-1)-2(x-1)=x(x+1)(x-1)-2(x-1)=(x-1)[x(x+1)-2]
daca x=a⇒(a-1)[a(a+1)-2]