Tuesday, December 2, 2014

completely factor the following expressions. z^2 + 15z - 54

We need to find two numbers that multiply to -54 and add to +15.


This means that one number will be negative and one will be positive.  (a negative times a positive is negative)


Also the larger of the two numbers will be positive, since when added it results in a positive number.


Let us list the factors of -54 that fit this criteria.


-1*54 = -54.


-2*27 = -54


-3 * 18 = -54. and hey! 18 + -3 = 15


So our answer is (x - 3)(x + 18)

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