You need to know this cold: if r is a root of polynomial p(x), then x-r divides p(x) evenly (i.e. no remainder) AND  p(r) = 0.   



These facts will be used countless times from Algebra on up the mathematics subjects. 



Example: find the roots of 



  ---> p(x)/(x-2) = x-7    (no remainder)

x=7 is one root

x=2 is the 2nd root  (the total count of roots always equals the highest power found in p(x), here we have two roots because the highest power of x in p(x) is 2) 

 

p(7) = 7^2-9(7)+14 = 49-63+14 = 0   <<< p(7) = 0 as expected

check p(2) on your own. 



 

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