Question

Rozłóż wielomian w na czynniki: a) w(x)=x^4+6x^3+11x^2+6x b) w(x)=x^6+7x^5+6x^4

Answer 1

a)

w(x)=x^4+6x^3+9x^2+2x^2+6x

w(x)=x^2(x^2+6x+9)+2x(x+3)

w(x)=x^2(x+3)^2+2x(x+3)

w(x)=(x+3)(x^3+3x^2+2x)

w(x)=x(x+3)(x^2+3x+2)

                   Δ=9-8=1

                x₁=-2      x₂=-1

w(x)=x(x+3)(x+2)(x+1)

 

b)

w(x)=x^6+7x^5+6x^4

w(x)=x^4(x^2+7x+6)

                 Δ=49-24=25   √Δ=5

                x₁=-6      x₂=-1

w(x)=x^4(x+1)(x+6)