Question

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Prosze o rozwiązanie. Ważne

Answer 1

a) W(x) = x^3 + x^2 + 3x + 3

    W(x) = x^2(x + 1) + 3(x+1)

    W(x) = (x+1)(x^2+3)

    W(x) = (x+1)(x+√3)(x-√3)

 

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

    W(x) = x^2(x+4) -4(x+4)

    W(x) = (x+4)(x^2-4)

    W(x) = (x+4)(x+2)(x-2)

 

d)  W(x) = 2x(x-3) + 4x(x-3)

     W(x) = (x-3)(2x + 4x)
     W(x) = (x-3)(6x)

 

 

2.

a)  x^3 + x^2 + 4x + 4 = 0

x^2(x+1) + 4(x+1) = 0

(x+1)(x^2 + 4) = 0

x + 1 = 0   lub   x^2 + 4 = 0

x = -1                brak rozwiązań

 

odp: x=-1

 

b) x^3 + x^2 - 9x - 9 = 0

x^2(x+1) -9(x+1) = 0

(x+1)(x^2 - 9) = 0

(x+1)(x - 3)(x+3) = 0

x=-1   x=3    x=-3

 

c) x^2 + 9 = 0

(x+3)(x-3) = 0

x=-3   x=3

 

d) x^3 - x^2 - 2x = 0

x(x^2 - x - 2) = 0

x = 0   lub   x^2 - x - 2 = 0

                  Δ = 1 + 8 = 9

                  √Δ = 3

                  x1 = -4/2 = -2

                  x2 = 2/2 = 1