Mathematics

Problem

The cubic polynomial

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

obeys the following conditions: • When divided by

x-1

, the remainder is

10

. • When divided by

x-2

, the remainder is

4

. •

x+1

is a factor of

p(x)

. Proceed with the tasks below. a. (i) Frame three equations in

a

b

and

c

corresponding to the above conditions. b. (ii) Solve these equations to find the values of

a

b

and

c

. c. (iii) Using the obtained coefficients, write

p(x)

as a product of linear factors.