Question

HELP PLEASE!!! write a polynomial function in standard form using the given information: p is a degree of 3; p(0)=-96; zeros: -3, 4i. steps please?

Answer 1

\[p(x)=a(x+3)(x-4i)(x+4i)\] second two factors multiply out to \((x^2+16)\) so start with
\[p(x)=a(x+3)(x^2+16)\]

Answer 2

then since you know \(p(0)=-96\) you have
\[-96=p(0)=a(0+3)(0+16)=48a\] which tells you that \[-96=48a\] or \[a=-2\] therefore it is
\[p(x)=-2(x+3)(x^2+16)\] or whatever you get when you multiply that out

Answer 3

thank youuuu! :)