SOLUTION: ax^3+bx^2+x-6 has factor (x+2) and (x-2) then in both cases remainder is 4 then find the value of a and b? thanks if anybody can solve it for me

Question 799653: ax^3+bx^2+x-6 has factor (x+2) and (x-2) then in both cases remainder is 4 then find the value of a and b? thanks if anybody can solve it for me
Answer by josgarithmetic(39623) (Show Source): You can put this solution on YOUR website!
Many details to the process, but you would want to do synthetic division using "divisors" of x+2, and of x-2, each separately. The roots correspondingly being checked are -2 and +2.

The dividend would be one of the factors of , once a has been factored. This dividend is . During the division, the intermediary expressions become more complicated...

The root, -2 gives remainder , equated according to the description of the problem; and the root +2 gives remainder .
These seem to be two equations in the unknowns, a and b.

Finishing the solution for a and b from here should be no trouble, seems to appear straightforward.
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