Evaluating $2x^3-9x^2-10x+13$ for $x=3+\sqrt{5}$. Is there an efficient way to tell that this reduces to $1$? I was helping my sibling with a math problem from a past year paper for a competitive exam. It requires us to evaluate this cubic expression for a given value of $x$ which has an $a+b$ form where $b$ is a square root, as shown:

I essentially plugged in $x=a+b$ in the expression and expanded each term and finally got the answer as $1$. But this does not seem like the fastest way to do this, especially because there is only 1 minute given to solve each multiple choice question.
Is there a better way to reduce the original expression that gives the answer as $1$ or suggests that the square root term is going to evaluate to $0$?
Thanks!

if $5 = (x-3)^2$ then $-10x = -2x(x-3)^2 = -2x^3+12x^2-18x$
Substituting this into $2x^3 - 9x^2 - 10x + 13$
we have
$$\begin{align}
2x^3 - 9x^2 +(-2x^3+12x^2-18x) + 13 &= 3x^2-18x+13\\
&= 3x^2-18x+27-14\\
&= 3(x^2-6x+9)-14\\
&= 3(x-3)^2-14\\
&= 3\cdot 5-14\\
&= 15-14\\
&= 1\\
\end{align}$$
