SAT Question ffdbcad4: Equivalent Expressions answer and explanation with Desmos solution

Choice D is correct. It's given that $4x^2+bx-45$ can be rewritten as $\left(hx+k\right)\left(x+j\right)$. The expression $\left(hx+k\right)\left(x+j\right)$ can be rewritten as $h{x}^2+jhx+kx+kj$, or $h{x}^2+\left(jh+k\right)x+kj$. Therefore, $h{x}^2+\left(jh+k\right)x+kj$ is equivalent to $4x^2+bx-45$. It follows that $kj=-45$. Dividing each side of this equation by $k$ yields $j=\frac{-45}{k}$. Since $j$ is an integer, $-\frac{45}{k}$ must be an integer. Therefore, $\frac{45}{k}$ must also be an integer.