1.
a)
W(x)=x³-x²+x-1=x²(x-1)+(x-1)=(x-1)(x²+1)
b)
W(x)=9x³-4x²-27x+12=x²(9x-4)-3(9x-4)=(9x-4)(x²-3)=(9x-4)(x+√3)(x-√3)
2.
a)
P(x)=2x³-6x²
P(x)=0
2x³-6x²=0 |:2
x³-3x²=0
x²(x-3)=0
x²=0 ∨ x-3=0
x=0 - pierwiastek podwójny ∨ x=3
x∈{0,3}
b)
P(x)=5(x-2)+x(x-2)
P(x)=0
5(x-2)+x(x-2)=0
(x-2)(5+x)=0
x-2=0 ∨ 5+x=0
x=2 ∨ x=-5
x∈{-5,2}
c)
P(x)=(x+1)²-3(x+1)
(x+1)²-3(x+1)=0
(x+1)(x+1-3)=0
(x+1)(x-2)=0
x+1=0 ∨ x-2=0
x=-1 ∨ x=2
x∈{-1,2}
d)
P(x)=2x³+x²-2x-1
2x³+x²-2x-1=0
x²(2x+1)-(2x+1)=0
(2x+1)(x²-1)=0
(2x+1)(x+1)(x-1)=0
2x+1=0 ∨ x+1=0 ∨ x-1=0
2x=-1 |:2 ∨ x=-1 ∨ x=1
x=-1/2 ∨ x=-1 ∨ x=1
x∈{-1,-1/2,1}