Question

1.Rozłóż wielomian na czynniki:

a) w(x)= + - 4 - 4x

b) w(x)= 5 + - 15x - 3

2. Rozwiąż równanie:

a) 81 -9 - 9x + 1= 0

Answer 1

zad1

a) W(x)=x4 + x3 -4x2 - 4x

W(x)= x3(x+1) -4x(x+1)

W(x)= (x+1)(x3-4x)

W(x)=x(x2-4)(x+1)

W(x)=x(x-2)(x+2)(x+1)

 

b) W(x)= 5x3 +x2 -15x -3

W(x)=x2(5x+1) -3(5x+1)

W(x)=(5x+1)(x2-3)

W(x)=(5x+1)(x-√3)(x+√3)

 

zad.2

a) 81x3 -9x2 -9x +1=0

9x2(9x-1)  - (9x-1) =0

(9x -1)(9x2 -1)=0

(9x-1)(3x+1)(3x-1)=0

Answer 2

zad 1

a)

W(x)=x⁴+x³-4x²-4x
W(x)= x³(x+1)-4x(x+1)
W(x)=(x³-4x)(x+1)
W(x)=x(x²-4)(x+1)
W(x)=x(x-2)(x+2)(x+1)

b)

W(x)= 5x³+x²-15x-3
W(x)=x²(5x+1)-3(5x+1)
W(x)=(x²-3)(5x+1)
W(x)=(x-√3)(x+√3)(5x+1)

zad 2

a)

81x³-9x²-9x+1=0
9x²(9x-1)-(9x-1) =0

(9x² -1) (9x-1)=0
(3x+1)(3x-1)(9x-1)=0

 

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