Polynomial `P(x)` is divided by `(x-3)` , the remainder if 6.If `P(x)` is divided by `(x^2-9)` , then the remainder is `g(x)` . Then the value of `g(2)` is ___________.

Answer

`4`

Explanation

As `P(x)` has only add degree terms
`:. P(-x) = -P(x)`
`rArr P(-3) = -P(3) = -6`
Let `P(x) = Q(x^(2) - 9) + g(x)`
where `Q` is quetient and `g(x)` is remainder `g(x) = ax + b`
`P(x) = Q(x^(2)- 9) + ax + b`
`x = 3, P(3) = 3a + b = 6 ….(i)`
`x = -3, P(-3) = -3a + b = -6 ....(ii)`
`b = 0` and `a = 2`
`:. g(x) = 2x`
`:. g(2) = 4`