[tex]zad.1\\\\a)\\\\W(x)=16x^{2} -49\\\\W(x)=(4x)^{2} -7^{2} \\\\W(x)=(4x-7)\cdot (4x+7)[/tex]
Korzystam ze wzoru skróconego mnożenia:
x² - y² = ( x - y ) × ( x + y )
[tex]b)\\\\W(x)=2x^{3} +5x^{2} -3x\\\\W(x) = x\cdot ( 2x^{2} +5x-3)\\\\f(x)=2x^{2} +5x-3 ~~-~~obliczam~~\Delta\\\\a=2,~~b=5,~~c=-3\\\\\Delta=b^{2} -4ac\\\\\Delta=5^{2} -4\cdot 2\cdot (-3)=25+24=49,~~\sqrt{\Delta} =7\\\\\Delta > 0~~\Rightarrow~~funkcja~~kwadratowa~~f(x)~~posiada~~dwa~~rozwiazania\\\\x_{1} =\dfrac{-b-\sqrt{\Delta} }{2a} ~~\lor~~x_{2} =\dfrac{-b+\sqrt{\Delta} }{2a} \\\\[/tex]
[tex]x_{1} =\dfrac{-5-7 }{2\cdot 2} ~~\lor~~x_{2} =\dfrac{-5+7}{2\cdot 2} \\\\x_{1} =-3~~\lor~~x_{2}=\dfrac{1}{2} \\\\f(x)=2(x+3)\cdot (x-\dfrac{1}{2} )\\\\W(x)=2x\cdot (x+3)\cdot (x-\dfrac{1}{2})[/tex]
