Maths ERGENT HW!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!20pts

a. The highest possible degree of the remainder is 1



b. Let P(x) = (x - 1)(x + 2)Q(x) + (ax + b)

where Q(x) is a polynomial

a and b are constants


By remainder theorem,

f(1) = -4

So, a + b = -4

f(-2) = -28

So, -2a + b = -28


Solving the two equations,

a = 8

b = -12


So, when P(x) is divided by (x - 1)(x + 2),

the remainder is 8x - 12