Rozkład wielomianu na czynniki Treść zadania w załączniku. Przykład f)

[latex]\f) \W(x)= frac{1}{4}x^3 (3x^2-5x-2)= frac{1}{4} x^3(3x^2-6x+x-2)= \ \ frac{1}{4} x^3*[3x(x-2)+(x-2)]= frac{1}{4} x^3(x-2)(3x+1)[/latex]

[latex]f)\\W(x) = frac{3}{4}x^{3}-frac{5}{4}x^{4}-frac{1}{2}x^{3}=frac{1}{4}x^{3}(3x^{2}-5x-2) =\\=frac{1}{4}x^{3}(3x^{2}-6x+x-2) = frac{1}{4}x^{3}[3x(x - 2) + (x-2)]=\\=frac{1}{4}x^{3}(3x+1)(x-2)[/latex] LUB [latex]3x^{2}-5x-2 = 0\\Delta = (-5)^{2}-4*3*(-2) = 25+24 = 49\sqrtDelta} = 7\\x_1 = frac{5-7}6} = -frac{1}{3}\x_2 = frac{5+7}{6}= 2\\3x^{2}-5x-2 = 3[x-(-frac{1}{3})](x-2)=3(x+frac{1}{3})(x-2) = \\=3(x^{2}-2x+frac{1}{3}x-frac{2}{3})=3x^{2}-6x+x-2= 3x(x - 2)+(x-2)=\\=(3x+1)(x-2)[/latex] [latex]W(x) = frac{3}{4}x^{5}-frac{5}{4}x^{4}-frac{1}{2}x^{3}=frac{1}{4}x^{3}(3x^{2}-5x-2)=\\=frac{1}{4}x^{3}(3x+1)(x-2)[/latex]