Let (35x-29)/(x^2-3x+2) =(N_1)/(x-1)+(N_2)/(x-2) be an identity in x. The numerical value of N_1N_2 is:

1966 AMC 12 Problem 7

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Let

\frac{35x-29}{x^2-3x+2} =\frac{N_1}{x-1}+\frac{N_2}{x-2}

be an identity in

x.

The numerical value of

N_1N_2

is:

-246

-210

-29

210

246

Combine the two fractions over

(x-1)(x-2)

Compare the coefficient of

x

and the constant term

Combining the right side gives numerator

\begin{aligned} &N_1(x-2)+N_2(x-1)\\ &\quad=(N_1+N_2)x\\ &\qquad-(2N_1+N_2). \end{aligned}

Thus

N_1+N_2=35

and

2N_1+N_2=29.

Hence

N_1=-6,

N_2=41,

and

N_1N_2=-246.

Therefore, the correct answer is A.