Question

Given the polynomial is exactly divided by x + 1,
and when it is divided by 3x - 1, the remainder
is 4. The polynomial gives a remainder hx + k when
divided by 3x2 + 2x - 1 then the values of h and
k are

Answer 1

Givens:

P(x)=Q1(x)⋅(x+1) [note here that P(−1)=0]

and

P(x)=Q2(x)⋅(3x−1)+4 [note here that P(13)=4]

Need to determine h,k where:

P(x)=Q3(x)⋅(x+1)(3x−1)+hx+k

P(−1)=0⟹−h+k=0⟹h=k.

P(13)=4⟹h3+k=4⟹4h3=4⟹h=k=3.

Answer 2

Polynomial is not given