Question

rozłoz wielomiany na czynniki x do potegi 3-4x+3

Answer 1

x³ -4x+3

x³-3x -x+3

x³-x -3x+3

x(x²-1) -3(x-1)

 

x(x-1)(x+1) -3(x-1)

(x-1)(x(x+1) -3)

(x -1)(x²+x -3)

        Δ=1 +12=√13

         x₁=(-1+√13)/2=½(-1+√13)

         x₂=(-1-√13)/2=½(-1-√13)

(x - 1)(x -½(-1+√13))(x- ½(-1-√13))

 

Answer 2

W(x)= x³-4x+3

W(1)=0

 

x³-4x+3 :(x-1)= x²+x-3

-x³+x²

-----

x²-4x

-x²+x

------

   3x+3

    -3x-3

    -------

     ====

 

W(x)= (x²+x-3)(x-1)

Δ= 1-4*1*(-3)

Δ= 13   √Δ= √13

 

x1= (-1-√13)/2

x2= (-1+√13)/2

x3= 1

 

W(x)= [x-(-1-√13)/2][x-(-1+√13)/2][x-1]