Consider the quadratic polynomial
p(x)=x2+(k−3)x+k.
It satisfies the following conditions:
• It is exactly divisible by x−2.
• It leaves a remainder of 4 when divided by x+1.
Work through the tasks given below.
(i) Write two equations in k corresponding to the given conditions.
(ii) Solve the equations to determine k.
(iii) For the calculated value of k, factorise p(x) completely.