Question

1. Rozłóż na czynniki.
a) 5x^3-3x^2-15x+9
b)x^2+x-y-y^2

Answer 1

A) 5x^3 - 3x^2 - 15x +9 
5x(x2 - 3) -3(x2 - 3) = 0
(x2-3)(5x-3)=0
(x-pierwiastek z 3)(x+pierw3)(5x-3)=0 
x = pierwiastek z 3 ; x = -pierwiastek z 3 ; 5x = 3
                                                              x = 3/5

Answer 2

a) 5x^3-3x^2-15x+9 = x^2(5x - 3) - 3(5x - 3) = (5x - 3)(x^2 - 3) = (5x - 3)(x -√3)(x +√3)
 
b)x^2+x-y-y^2 = x^2 - y^2 + x - y = (x - y)(x + y) + (x - y) = (x - y)(x + y + 1)