The polynomial depends on real constants and

MATHEMATICS · Subjective · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions

Problem

The polynomial

F(x)=x^5+ax^4+bx^3+cx^2+dx

depends on real constants

a, b, c,

and

d

. For each case below, state the condition(s) on the constants so that

F(x)

satisfies the required symmetry: (i)

F(x)

is an even function. (ii)

F(x)

is an odd function.