Zad.1 Wykonaj działanie na wielomianach   2W(x)-P(x)*Q(x), gdzie: w(x)=x4+2x2-5 p(x)=2x-1 q(x)=x3+x-4     Zad.2 Rozłóż wielomian W na czynniki:   a) W(x)= x3-x2-4x+4 b) W(x)=x3+x2+10x+10 c) W(x)=-x3-x2+3x+3

Zad.1 [latex]2w(x)-p(x)q(x)=2(x^4+2x^2-5)-(2x-1)(x^3+x-4)\ =2x^4+4x^2-10-(2x^4+2x^2-4x-x^3-x+4)\ =2x^4+4x^2-10-2x^4-2x^2+4x+x^3+x-4\ =x^3+2x^2+x-14[/latex] Zad.2 a) [latex]w(x)=x^3-x^2-4x+4=x^2(x-1)-4(x-1)\ =(x-1)(x^2-4)=(x-1)(x-2)(x+2)[/latex] b) [latex]w(x)=x^3+x^2+10x+10\ =x^2(x+1)+10(x+1)=(x+1)(x^2+10)[/latex] c) [latex]w(x)=-x^3-x^2+3x+3=-x^2(x+1)+3(x+1)\ =-(x+1)(x^2-3)=-(x+1)(x-sqrt(3))(x+sqrt(3))[/latex]