Rozłóż wielomian w na czynniki a)w(x)=2x^3+4x^2+2x b)w(x)=-3x^5+30x^3-75x będę wdzięczy za pomoc

[latex]a) W(x)=2x^{3}+4x^{2}+2x\ W(x)=2x(x^{2}+2x+1)\ W(x)=2x(x+1)^{2}\ \ Wzor: a^{2}+2ab+b^{2}=(a+b)^{2}\ \ \ b) W(x)=-3x^{5}+30x^{3}-75x\ W(x)=-3x(x^{4}-10x^{2}+25)\ W(x)=-3x[(x^{2})^{2}-2*x^{2}*5+5^{2}]\ W(x)=-3x(x^{2}-5)^{2}\ W(x)=-3x[(x-sqrt{5})(x+sqrt{5})]^{2}\ W(x)=-3x(x-sqrt{5})^{2}(x+sqrt{5})^{2}\ \ Wzory:\ a^{2}+2ab+b^{2}=(a+b)^{2}\ a^{2}-b^{2}=(a-b)(a+b)\ (a*b)^{2}=a^{2}*b^{2}[/latex]

a) W(x) = 2x³ + 4x² + 2x = 2x(x² + 2x + 1) = 2x(x + 1)(x + 1) x² + 2x + 1 = 0 Δ = 2² - 4 * 1 * 1 = 4 - 4 = 0 x₁ = x₂ = - 2/2 = - 1 b) W(x) = - 3x⁵ + 30x³ - 75x = - 3x(x⁴ - 10x² + 25) = = - 3x(x² - 5)(x² - 5) = - 3x(x - √5)(x + √5)(x - √5)(x + √5)  x⁴ - 10x² + 25 = 0 za x² wstawiamy z z² - 10z + 25 = 0 Δ = (- 10)² - 4 * 1 * 25 = 100 - 100 = 0 z₁ = z₂ = 10/2 = 5 x² = 5 x₁ = √5 , x₂ = - √5