Polynomial Divisibility

Let $$P(x) = 2x^4 - 3x^3 + 7x^2 - 5x + k$$ be a polynomial where the polynomial is divisible by $$x^2 - 2$$. What is the value of $$k$$?

You need to find the integer value of $$k$$ such that when you perform polynomial long division of $$P(x)$$ by $$x^2 - 2$$, the remainder is zero.