Let R1 and R2 be the remainders

Question

when polynomials x^3 + 2x^2 - 5ax
- 7 and x^ 3 + ax^2 - 12 x + 6 are
divided by ( x + 1 ) and ( x - 2 )
respectively. If 2R1 + R2 = 6, find
a. Please work the complete solution.

Answer 1

if x+1 is a factor, then f(-1) = 0 from the first function:
f(-1) = -1 + 2 -5a(-1) - 7 = R1
R1 = 5a -6

if x-2 is a factor of the second function
f(2) = 8 + 4a - 24 + 6
= 4a - 10 = rR2

R1 + R2 = 6
5a-6 + 4a-10 = 6
9a = 22
a=22/9

Answer 2

Got you wrong for this time, (x+1) and (x+2) aren't factors, they leave remainder R1 and R2 stated clearly at the top, by the way, Thanks for help, I've solved this question and the value of a is 2.

Answer 3

Actually you solved it correctly but its 2R1, so you need to multiply your R1 by 2 and then equate it by 6. Little mistake but it won't fetch you marks in examinations.

Answer 4

Its the bad way to do the Question. I think you should try another.🤔