Quandaries and Queries


I got a problem with factorise the expression

Could you help me and send the solution as soon as possible.




Hi Dorota,

The easiest way to factor a cubic, if it works, is to find an integer root of the expression and then divide. This technique depends on finding an integer root.

Suppose that you can factor this expression using integers, then you would have

(2x - a)(x - b)(x - c) = 2x3+11x2-5x-50 For some integers a, b and c. Look at this expression for x = 0. The left side is (-a)(-b)(-c) anf the right side is -50. Thus abc = 50

This fact shows you where to look for integer roots. An integer root must be a divisor of 50. Thus the only possible integer roots are 1, 2, 5, 10, 25, 50 and the negatives of these 6 numbers. Substitute these numbers into the exprression to see if any of them is a root. If you find a root r then divide 2x3+11x2-5x-50 by (x - r) to get a quadratic.


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