How to find the values of a and b? If the polynomial 6x4 + 8x3 - 5x2 + ax + b is exactly divisible by the polynomial 2x2 - 5, then find the values of a and b.

You can just write $$6x^4 + 8x^3 - 5x^2 + ax + b=(2x^2-5)(Ax^2+Bx+C)$$ Expand the rhs to get $$6x^4 + 8x^3 - 5x^2 + ax + b=2Ax^4+2Bx^3+(2C-5A)x^2-5Bx-5C$$ Now identify the coefficients of the differents powers of $x$. Using $x^4,x^3,x^2$, this leads to $A=3$, $B=4$,$C=5$.
I am sure that you can take from here.
