1. [latex]a) (x^{3}-6x^{2}+4x-5)+(-x^{2}+4)= x^{3}-7x^{2}+3x-9 [/latex] [latex] b) (x^{3}-6x^{2}+4x-5)-(-x^{2}+4)= x^{3}-6x^{2}+4x-5-x^{2}-4=[/latex] =[latex]= x^{3}-7x{2}+3x-9[/latex] [latex]c) = -3x^{2}+12-2x^{3}+12x^{2}-8x+10=-2^{3}+9x^{2}-8x+24[/latex] [latex]d) =-x^{5}+4x^{3}+6x^{4}-24x^{2}-4x^{3}+16x+5x^{2}-20=[/latex] =[latex]=-x^{5}+6x^{4}+19x^{2}+16x-20[/latex] 2. [latex]a) 9x^{2}-36 |:9[/latex] [latex]x^{2}-3= (x-sqrt{3})(x+sqrt{3})[/latex] [latex] b) =(x^{2}-5)(x+3)=(x-sqrt{5})(x+sqrt{5})(x+3)[/latex] [latex]c) =(8x^{2}-sqrt{25})(8x^{2}+sqrt{25})=[/latex] [latex]=(sqrt{8}x-sqrt[3]{25})(sqrt{8}x+sqrt[3]{25) (8x^{2}+sqrt{25})[/latex] d[latex]d) =(x-5)(x^{2}+5x+25)[/latex] 3. [latex]x^{2}(x-5)+9(x-5)=0[/latex] [latex] =(x^{2}+9)(x-5)= [/latex] [latex]x=5 [/latex] [latex] b) x(6x^{2}+7x-13)=0[/latex] [latex] Delta= b^{2}-4*a*c = 7^{2}-4*6*(-13)=49+312=361[/latex] [latex]sqrt{delta}=19[/latex] [latex]x_{1}=frac{-7-19}{2*(-13)}=1 [/latex] [latex]x_{2}= frac{-7+19}{2*(-13)}=frac{12}{-26}=frac{6}{-13}[/latex] [latex] c) x^{2}(x-5)-16(x-5)=0[/latex] [latex](x^{2}-16)(x-5)=0[/latex] [latex](x-4)(x+4)(x-5)=0[/latex] [latex]x_{1}=4 [/latex] [latex]x_{2}=-4[/latex] [latex]x_{3}=5[/latex] [latex]d) (x^{2}-4)(x^{2}+4)=0[/latex] [latex](x-2)(x+2)(x^{2}+4)[/latex] [latex] x_{1}=2[/latex] [latex]x_{2}=-2[/latex]
