Question

ROZŁÓŻ WIELOMIANY NA CZYNNIKI NAJPROSTSZE:

a) W(x)=3x do 5-12x do 3

b)W(x)= - x do 5-12x do 4+ 9x +108

c)W(x)= x do 3 -2x do 2-8x

d)W(x)=3x do 3-24

Answer 1

a) W(x)=3x do 5-12x do 3 = 3x^3(x^2-4)=3x^3(x-2)(x+2)

 

b)W(x)= - x do 5-12x do 4+ 9x +108=x(9-x^4)+12(9-x^4)=(x+12)(3-x^2)(3+x^2)=

=(x+12)(V3-x)(V3+x)(3+x^2)

 

c)W(x)= x do 3 -2x do 2-8x=x(x^2-2x-8)=x(x-2)(x+4)

 

 d)W(x)=3x do 3-24=3(x^3-2^3)=(x-2)(x^2+2x+4)

Answer 2

a) W(x)=3x⁵-12x³= 3x³(x²-4)=3x³(x-2)(x+2)

 

b)W(x)= - x⁵-12x⁴+ 9x +108=x⁴(-x-12)-9(-x-12)=(-x-12)(x⁴-9)=(-x-12)(x²-3)(x²+3)(-x-12)(x-√3)(x+√3)(x²+3)

 

c)W(x)= x³ -2x²-8x=x(x²-2x-8)=x(x-4)(x+2)

Δ=(-2)²-4*1*(-8)=4+32=36

√Δ=6

x₁=(2+6)/2=8/2=4

x₂=(2-6)/2=-4/2=-2

 

 d)W(x)=3x³-24=3(x³-8)=3(x-2)(x²+2x+4)