Question

When (x+1)square is divided by x-2 the quotient is 16 and the remainder is x-3. Find the value of x

Answer 1

x^2+2x+1/x-2=16+(x-3/x-2)

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^2+2x+1=16*(x-2)+x-3

x^2+2x+1=16x-32+x-3

x^2+2x+1=17x-35

x^2+1=17x-2x-35

x^2+1=15x-35

x^2=15x-35-1

x^2=15x-36

x^2-15x+36

x^2-(15+3)

(X-3)(X-12)

X=3,X=12

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