Need help for this JC 1 polynomial question

Hello,

Please help me with this math question-!!

The polynomial f(x) has a factor (x -1) and leaves a remainder of 3 when divided by (x + 2).

Given that the following relation f(x +1) + f(x +4) = a is true for all real values of x, find the value of a.

I didn't understand the second part of the question and I am lost now so please help me.

Student X

f(1)=0 since x-1 is a factor and  f(-2)= 3 since f(x) yields a remainder of 3 when divided by x+2.

f(x +1) + f(x +4) = a is true for all values of x implies we can choose any value of x, substitute into the LHS expression and the RHS will always evaluate to the value of a.

So choosing x=-3,

f(-3+1) + f(-3+4) = f(-2) + f(1) = 3 + 0 = 3

Therefore, the value of a is 3. (shown)

Hope this helps. Peace.

Best Regards,

Mr Koh