Question

X² - c ÷ x-b

In the expression above, b and c are positive integers.
If the expression is equivalent to x+b and x≠b, which
of the following could be the value of c?

Answer 1

Answer: Choice A) 4

Reason:

If (x^2-c)/(x-b) = x+b, then we can rearrange things into this:

x^2-c = (x-b)(x+b) = x^2-b^2

I'm using the difference of squares rule.

Comparing terms, we see that b^2 = c.

If b is an integer, then c is a perfect square.

Of the answer choices listed, only 4 is a perfect square.