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If the rational number x= b/ c is a zero of the nth degree polynomial,
P ( x ) = sxn+ ...........+ t
Where every the coefficients are integers then b will be a factor of t & c will be a factor of s.
Note that in order for this theorem to work then the zero have to be reduced to lowest terms. In other terms it will work for 4/3 but not necessarily for 20/15.
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10x^7y^3 and 25xv^8y^4
Example : determine the zeroes of following polynomials. P ( x)= 5x 5 - 20x 4 +5x3 + 50x2 - 20x - 40 = 5 (x + 1) 2 ( x - 2) 3 Solution In this the factoring has been
(x+2) (x+3)
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Solve (3x+ 1/ x + 4 ) ≥ 1. Solution The first thing that we have to do here is subtract 1 from both of sides and then get everything in a single rational expression. (3
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