Let , where , and are real…

MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Let

p(x)=x^{3}+ax^{2}+bx+c

, where

a

b

and

c

are real numbers. (i) Show that the remainder obtained when

p(x)

is divided by

x-1

1+a+b+c

. (ii) Hence prove that

x-1

is a factor of

p(x)

if and only if

a+b+c=-1

. (iii) If

a=2

and

b=-3

, determine the value of

c

for which

x-1

is a factor of

p(x)