How do you find the factors of f(z)f(z) over C if f(z)=2z^3+3z^2-14z-15f(z)=2z3+3z214z15?

1 Answer
Sep 17, 2016

(z+1)(z+3)(2z-5)(z+1)(z+3)(2z5).

Explanation:

We observe that,

The Sum of the co-effs. of odd powered terms of zz is

2-14=-12214=12,

and, that of even powered, 3-15=-12315=12

We conclude that (z+1)(z+1) is a factor of f(z)f(z).

"Now, "f(z)=2z^3+3z^2-14z-15Now, f(z)=2z3+3z214z15

=ul(2z^3+2z^2)+ul(z^2+z)-ul(15z-15)

=2z^2(z+1)+z(z+1)-15(z+1)

=(z+1)(2z^2+z-15)

=(z+1){ul(2z^2+6z)-ul(5z-15)}

=(z+1){2z(z+3)-5(z+3)}

=(z+1)(z+3)(2z-5).