Question

Rozloz wielomian na czynniki:
1) (x+1)^2 -4
2) (x-3)^2 -x^2
3) (x^2-6)^3-8

Answer 1

A) x^2+2x+1-4=x^2+2x-3
delta=4+12=16
pierwiastekzdelta=4
x1=(-2-4)/2=-3
x2=(-2+4)/2=1
x^2+2x-3=(x+3)(x-1)

b) x^2-6x+9-x^2=9-6x=3(3-2x)

c) a^3 - b^3 = (a - b)(a^2 + ab + b^2)
(x^2-6)^3-2^3=(x^2-6-2)([x^2-6]^2+2(x^2-6)+4)=(x^2-8)(x^4-12x^2+36+2x^2-12+4)=
=(x^2-8)(x^4-10x^2+28)=(x-2√2)(x+2√2)(x^4-10x^2+28)