Polynomfunktion 3 Grades Produktform

Question

Was ist die Poduktform von f(x)=x^3+2x^2-4x?

f(x)=(x)(x-1,24)(x+3,24)

Answer 1

f(x) = x^3 + 2·x^2 - 4·x

f(x) = x·(x^2 + 2·x - 4)

f(x) = x·(x^2 + 2·x - 4)

x^2 + 2·x - 4 = 0 --> x = - 1 ± √5

f(x) = x·(x - (-1 + √5))·(x - (-1 - √5))

f(x) = x·(x + 1 - √5)·(x + 1 + √5)