Odpowiedź:
Zad 4.
[tex]a) (3x^{4} -2x^{3} +1)(2x-1)=6x^{5} -4x^{4} +2x-3x^{4} +2x^{3} -1=6x^{5} =7x^{4} +2x^{3} +2x-1\\b)(x^{4}+5x^{3}-3x^{2})(4-\frac{1}{2}x)=4x^{4}+20x^{3}-12x^{2} -\frac{1}{2}x^{5} -2\frac{1}{2} x^{4} +2\frac{1}{2}x^{3} =-\frac{1}{2}x^{5} +1\frac{1}{2}x^{4}+22\frac{1}{2}x^{3} -12x^{2} \\c) (4x^{6} -2x)(3x-1)(2x+8)=(4x^{6} -2x)(6x^{2} +24x-2x-8)=(4x^{6} -2x)(6x^{2} +22x-8)=24x^{8} +88x^{7} -32x^{6} -12x^{3} -44x^{2} -8x[/tex]
Zad.5
[tex]a)(3x-2)^{2} =9x^{2}-12x+4\\b)(3a+2x)^{2}=9a^{2}+12ax+4x^{2}\\c)(2x-\sqrt{5})^{2} =4x^{2} -4\sqrt{5}x+5\\d) (6-3x)^{2} =36-36x+9x^{2}[/tex]
Zad.6
[tex]a) W(x)=(x-2)(2-3x)(x+1)\\x-2=0\\ x=2 \\\\2-3x=0\\-3x=-2\\x=\frac{2}{3} \\\\x-1=0\\x=1b) W(x)=(9-x^{2} )(x-3)(2x+6)\\9-x^{2} =0\\x^{2} =9\\x=3 lub x= -3\\\\x-3=0\\x=3\\\\2x+6=0\\2x= -6\\x= -3\\c) W(x)=(x^{2} +4)(x^{2} -4)(x^{2} -7)\\x^{2} +4=0\\x^{2} \neq -4 falsz\\\\x^{2} -4=0\\x^{2} =4\\x=4lubx=-4\\\\x^{2} -7=0\\x^{2} =7\\x=7lubx=-7[/tex]
Zad.7
