SOLUTION: X is a number such that when ( x+1)² is divided by (X-2),the quotient is 16 and the reminder is (X-3).what are the values of X?

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Question 971206: X is a number such that when ( x+1)² is divided by (X-2),the quotient is 16 and the reminder is (X-3).what are the values of X?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E2%2B2x%2B1%29%2F%28x-2%29=16%2B%28x-3%29%2F%28x-2%29, a way of saying the same as the description. The rational expression for the left member must be 16 with a remainder x-3, and of course the denominator is x-2 for that remainder. Performing the division should not be necessary.

Multiply both members by x-2:

x%5E2%2B2x%2B1=16%28x-2%29%2Bx-3

x%5E2%2B2x%2B1=16x-32%2Bx-3

x%5E2%2B2x%2B1=17x-35

x%5E2%2B1=15x-35

x%5E2-15x%2B36=0, which seems factorable...

%28x-12%29%28x-3%29=0
x=3 or x=12