x cubed - 2x squared + 4x - 8 = 0, what are ALL the solutions? Solving Polynomial Equations

[@russelllomando8460]

nice lesson, thanks.

[@Stylux-z1p]

x³ - 2x² + 4x - 8 = 0 --> Factorization x²(x - 2) + 4(x - 2) = 0 --> group and factor out the common factor (x² + 4)(x - 2) = 0 --> factor out (x - 2) x² + 4 = 0 ∨ x - 2 = 0 x² = -4 x = ±√-4 --> using imaginary number i = √-1 x = √4 · √-1 = 2 · i = ±2i --------------------------------------------------- x - 2 = 0 x = 2 the roots of the polynomial are {2 , 2i, -2i}✅

[@tomtke7351]

x^3-2x^2+4x-8=0 (x^2)(x-2)+4(x-2)=0 (x^2+4)(x-2)=0 solutions (x^2+4)=0 and (x-2)=0 for x^2+4=0 x= +/-sqrt(-4) = +/-2i sol.1 sol.2 for x-2=0 x = 2 sol.3

[@palmerreising3387]

Neat. It would have been helpful to have had such video presemtations in high school.

[@uyereogheneochuko9116]

😮😊🎉