Given that `x^2+x-6` is a factor of `2x^4+x^3-ax^2+b x+a+b-1,` find the value of `a and b dot`

Explanation

We have,
` x^(2) + x - 6 = (x+3)(x-2)`
Let `f(X)=2x^(4)+x^(3)-ax^(2)+bx + a + b -1`
Now, `f(-3) = 2 (-3)^(4)+ (-3)^(3)-3b + a+b - 1 = 0 `
or 134 - 8a -2b = 0
or 4a + b = 67 (1)
Now `f(2)=2(2)^(4) + 2^(3)-a(2)^(2)+2b+ a + b - 1 = -0`
or 39 - 3a + 3b = 0
or a - b = 13 (2)
From (1) and (2), a = 16, b= 3.