The polynomial depends on the real constants and .

MATHEMATICS · Multi-part · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions

Problem

The polynomial

h(x)=ax^{3}+(2a-1)x^{2}+bx

depends on the real constants

a

and

b

. (i) Find all values of

a

and

b

for which

h(x)

is an odd function. (ii) Find all values of

a

and

b

for which

h(x)

is an even function. (iii) For

a=2

and

b=-3

, classify

h(x)

as even, odd, or neither, giving a clear reason for your answer.