To solve this problem, what we have to do is to divide
the whole equation 4 x^4 – 2 x^3 – 6 x^2 + x – 5 with the equation 2 x^2 +
x – 1. Whatever remainder we get must be the value that we have to subtract from
the main equation 4 x^4 – 2 x^3 – 6 x^2 + x – 5 for it to be exactly divisible
by 2 x^2 + x – 1.
By using any method, I used long division we get a
remainder of -6.
Therefore we have to subtract -6 from the main equation
which results in:
4 x^4 – 2 x^3 – 6 x^2 + x – 5 – (-6) = 4 x^4 – 2 x^3 – 6 x^2
+ x + 1
