Mathematics

Problem

Let

r(x)=x^3+ax^2+bx+6

. It is known that

r(x)

is divisible by both

(x-1)

and

(x+2)

. a. (i) Form the equation obtained by substituting the appropriate value of

x

for the first factor. b. (ii) Form the equation obtained by substituting the appropriate value of

x

for the second factor. c. (iii) Solve the simultaneous equations obtained in parts (i) and (ii) to find the values of

a

and

b