Question

Rozłóż wielomian na czynniki i wyznacz jego pierwiastki
w(x)=x^3-4x^+2x-8
w(x)=x^3+x^2-9x-9
w(x)=x^3-3x^2-6x+18
w(x)=x^3+2x^2-3x-6

Answer 1

Odpowiedź:

1.

w(x)=x^3-4x^2+2x-8

x^3 - 4 x^2 + 2 x - 8 = 0

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

x - 4 = 0 lub x^2 + 2 = 0

x = 4 lub x^2 + 2 = 0

x = 4 lub x^2 = -2

x = 4

2.

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

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

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

x - 3 = 0 lub x + 1 = 0 lub x + 3 = 0

x = 3 lub x + 1 = 0 lub x + 3 = 0

x = 3 lub x = -1 lub x + 3 = 0

x = 3 lub x = -1 lub x = -3

3.

w(x)=x^3-3x^2-6x+18

x^3 - 3 x^2 - 6 x + 18 = 0

(x - 3) (x^2 - 6) = 0

x - 3 = 0 lub x^2 - 6 = 0

x = 3 lub x^2 - 6 = 0

x = 3 lub x^2 = 6

x = 3 lub x = √6 lub x = -√6

4.

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

x^3 + 2 x^2 - 3 x - 6 = 0

(x + 2) (x^2 - 3) = 0

x + 2 = 0 lub x^2 - 3 = 0

x = -2 lub x^2 - 3 = 0

x = -2 lub x^2 = 3

x = -2 lub x = √3 lub x = -√3