Let $\frac {35x - 29}{x^2 - 3x + 2} = \frac {N_1}{x - 1} + \frac {N_2}{x - 2}$ be an [identity](https://artofproblemsolving.com/wiki/index.php/Identity) in $x$. The numerical value of $N_1N_2$ is:
$\text{(A)} \ - 246 \qquad \text{(B)} \ - 210 \qquad \text{(C)} \ - 29 \qquad \text{(D)} \ 210 \qquad \text{(E)} \ 246$
\[\frac {N_1}{x - 1} + \frac {N_2}{x - 2} = \frac{N_1(x-2) + N_2(x-1)}{(x-1)(x-2)} = \frac{(N_1 + N_2)x - (2N_1 + N_2)}{x^2 - 3x + 2}\]
Comparing [coefficients](https://artofproblemsolving.com/wiki/index.php/Coefficient), we have the system of two equations
\begin{align*} N_1 + N_2 &= 35\\ N_1 + 2N_2 &= 29 \end{align*}
Subtracting the first equation from the second yields $N_2 = -6$. Substituting yields $N_1 = 41$, and their product is $-246 \Rightarrow \mathrm{(A)}$.