Question

p (p - 3 )^{2} - 4 (p - 3 )^{3} = 0 ayuda con esta ecuacion de tercer grado por factorizacion garcias

Answer 1

p(p-3)^2-4(p-3)^3=0
(p-3)^2[p-4(p-3)]=0
(p-3)^2(p-4p+12)=0
(p-3)^2(12-3p)=0
3(p-3)^2(4-p)=0
de donde (p-3)^2=0    p1=p2=3
      y          4-p=0        p3=4

Answer 2

Mari,
Vamos paso a paso

Efectuando productos notables
          p(p^2 - 6p + 9) - 4(p^3 - 9p^2 + 27p - 27) = 0

          p^3 - 6p^2 + 9p - 4p^3 + 36p^2 -108p + 108 = 0

Reduciendo terminos semejantes
       - 3p^3 + 30p^2 - 99p - 108 = 0

Factorizando
          −3(p - 4)(p - 3)^2 = 0

Determinando raices (tercer grado - 3 raices)
                                  p - 4 = 0
                                                      p1 = 4
                                  p - 3 = 0
                                                      p2 = p3 = 3

                                                                      S = {3, 4}