Question

Rozloz wielomian na czynniki:

w(x)= 2x^5-4x^4+x3
w(x)=7x^3+2x^2-28x-8

Answer 1

W(x)= 2x⁵ - 4x⁴ + x³ = x³(2x² - 4x +1) = 2x³(x - (2 - √2 / 2))(x - (2 + √2 / 2))
                         Δ = 16 - 8 = 8,  √Δ=2√2
x1 = 4 - 2√2 / 4 = 2 - √2 / 2,   x2 = 2 + √2 / 2

w(x)=7x³ +2x² - 28x - 8 = (metoda grupowania wyrazów) =
= x²(7x + 2) - 4(7x + 2) = 
=(x² - 4)(7x + 2) =  (wzory skróc. mnożenia) =
= (x + 2)(x - 2)(7x + 2)