Question

DESCOMPUNETI:x^5 + x^3 - x^2 - 1=
x^3 + x^2 - 4x+4=
x^2-12x-13=
x^2 + x - 2=
x^2+3x-10=
x^2+7x-18=
x^3-2x^2-x+2=
x^3-3x^2-4x+12=
x^3-x^2-9x+9=
x^3-4x^2-4x+16=
x^3+3x^2-16(x+3)=
4x^2-9-2(2x-3)=
4x^3+4x^2-9(x+1)=
9x^3+9x^2-x-1=
DESCOMPUNETI IN PRODUS DE FACTORI PRIMI:
x^2+2x-35=
x^2+6x-16=
x^2-6x-7=
x^2-6x-16=

Answer 1

x^2+3x-10= x^2+5x-2x-10=x(x+5)-2(x+5)=(x+5)(x-2)

x^2+7x-18= x^2+9x-2x-18=x(x+9)-2(x+9)=(x+9)(x-2)

x^5 + x^3 - x^2 - 1=x^2(x^3-1)+(x^3-1)=(x^3-1)(x^2+1)=(x-1)(x^2+x+1)(x^2+1)

 x^2-12x-13=(x^2-1)-12(x+1)=(x+1)(x-1)-12(x+1)=(x+1)(x-1-12)=(x+1)(x-13)

x^2 + x - 2= x^2-1+x-1=(x+1)(x-1)+x-1=(x-1)(x+1+1)= (x-1)(x+2)

x^3-2x^2-x+2=x(x^2-1)-2(x^2-1)=(x-2)(x+1)(x-1)

x^3-3x^2-4x+12=x(x^2-4)-3(x^2-4)=(x+2)(x-2)(x-3)

x^3-x^2-9x+9= x(x^2-9)-(x^2-9)=(x+3)(x-3)(x-1)

x^3-4x^2-4x+16=x(x^2-4)-4(x^2-4)=(x+2)(x-2)(x-4)

x^3+3x^2-16(x+3)= x^2(x+3)-16(x+3)=(x+3(x+4)(x-4)

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

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

9x^3+9x^2-x-1=9x^2(x+1)-(x+1)=(x+1)(9x^2-1)=(x+1)(3x+1)(3x-1)


x^2+2x-35= x^2-5x+7x-35=x(x-5)+7(x-5) =(x-5)(x+7)

x^2+6x-16= x^2-2x+8x-16=x(x-2)+8(x-2)=(x-2)(x+8)

x^2-6x-7= x^2-7x+x-7=x(x-7)+(x-7)=(x-7)(x+1)

x^2-6x-16= x^2+2x-8x-16=x(x+2)-8(x+2)=(x+2)(x-8)