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This problem trains for: SAT-I, AMC-8, GMAT, AMC-10.

Find the product of the numbers m and n such that the algebraic fraction:

equation

is reducible by the factor:

equation

Both the numerator and the denominator have to have a factor of x+2.

Both polynomials are quadratic and must have one linear factor. Therefore each must have two linear factors.

Since the leading coefficients are known, the unknown factor at the numerator must be of the form:

equation

but to obtain the desired constant term, we need:

equation

equation

equation

equation

Similarly, the denominator must be:

equation

equation

equation

The product of m and n is:

equation