Question

1.rozloz wielomian na czynniki a)w(x)=x^2-4 b)w(x)=8x^3-12x^2+6x-1 c)w(x)=x^3+3x^2+x+3 d)w(x)=x^2-5 e)w(x)=1/27+x^3 f)w(x)=9x^2-6x+1 g)w(x)=2x^3+8x^2+5x+20 2.jezeli wielomiany P(x)=x^2+bx-21 i Q(x)=(x-3)(x+7) sa rowne ile wynosi b ??

Answer 1

a)w(x)=x^2-4  =(x -2 )(x+2) 

b)w(x)=8x^3-12x^2+6x-1 = (2x -1)^3 

c)w(x)=x^3+3x^2+x+3 = x^2( x+3)+ (x+3)= (x^2 +1)(x+3)

d)w(x)=x^2-5 = (x - pier z 5)(x+ pier z 5) 

e)w(x)=1/27+x^3 = (1/3 + x)( 1/9 - 1/3 x + x^2) 

f)w(x)=9x^2-6x+1 = (3x - 1) ^2

g)w(x)=2x^3+8x^2+5x+20=2x^2(x +4) + 5(x +4)= (2x^2 + 5)(x+4) 

 

Zad2.

P(x)= Q(x) 

x^2 +bx -21 = (x-3)(x+7) 

x^2 +bx -21 = x^2 - 3x +7x -21 

x^2 +bx -21 = x^2 +4x - 41 

 bx = 4x  

 b = 4