factoring e^4 - 5e^2 - 5ef + ef^3 (can't get book's answer)

[kathleenjoelle]

e^4-5e^2-5ef+ef^3
ok so I know I factor out the e

e(e^3-5e-5f+f^3)

now I factor by grouping

e(e+f)(e^2-ef+f^2)-5(e+f)

so the (e+f) is common factor

and I end up with e(e+f)(e^2-ef+f^2)-5

BUT THE ANSWER IN THE BOOK IS DIFFERENT... How does the -5 end up in the brackets? It just does or what?
Books Answer:
e(e+f)(e^2-ef+f^2-5)

 

[Deleted member 4993]

Re: Need help factoring polynomials

e^4-5e^2-5ef+ef^3
ok so I know I factor out the e

e(e^3-5e-5f+f^3)

now I factor by grouping

e[(e+f)(e^2-ef+f^2)-5(e+f)]

so the (e+f) is common factor - and take it out of []

=e(e+f)[(e^2-ef+f^2) - 5]

do you see it now....


so the (e+f) is common factor

and I end up with e(e+f)(e^2-ef+f^2)-5

BUT THE ANSWER IN THE BOOK IS DIFFERENT... How does the -5 end up in the brackets? It just does or what?
Books Answer:
e(e+f)(e^2-ef+f^2-5)