Rozłóż wielomian na czynniki a)x3+4x2+x+4 b)6x3-5x2+6x-5 c)x3-1/2x2+x-1/2 d)x3-5x2+3x-15

a)   [latex]x^3+4x^2+x+4=x^2(x+4)+1(x+4)=(x+4)(x^2+1)[/latex]   b)   [latex]6x^3-5x^2+6x-5=6x(x^2+1)-5(x^2+1)=(x^2+1)(6x-5)[/latex]   c)   [latex]x^3-frac12x^2+x-frac12=x(x^2+1)-frac12(x^2+1)=(x^2+1)(x-frac12)[/latex]   d)   [latex]x^3-5x^2+3x-15=x(x^2+3)-5(x^2+3)=(x^2+3)(x-5)[/latex]