when `x^5-5*x^4+9*x^3-6*x^2-16*x+13` is divided by `x^2-3*x+a`, then quotient and remainder are `x^3-2*x^2+x+1` and `-15*x+11`, respectively, the value of a is:

Explanation

`x^5 - 5x^4 + 9x^3 - 6x^2 - 16x + 13 = (x^2-3x+a)(x^3 - 2x^2 + x+1) + (-15x + 11)`

`= x^5 - 2x^4 - 3x^4 + x^3 + 6x^3 + ax^3+ x^2 - 3x^2 - 2ax^2`

comparing both sides for `x^3`, we get

`(a+6+1) = 9`

`a+ 7 = 9`

`a = 2`

comparing both sides for `x^2`, we get

`-2 - 2a = -6`

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