Quandaries
and Queries 

Who is asking: Parent Level: Secondary Question: 

Hi, I assume that you arrived at x = 2 by just looking at the problem and realizing that 2^{2} = 4 and that 2 + 2 = 4. This is something that we try to get students to do, use their ingenuity and number sense. One drawback with this method however is that you may miss something. That is the situation here as x = 1 is also a solution. The procedural way to approach this problem is to first move the x term and the constant term to the left of the equal sign
and then factor the left side. Hence I want to find numbers a and b so that
If you expand the right side you will see that the constant term is a b and hence a b = 2. If a and b are integers then they must be 1 and 2 or 1 and 2. Try them
But you need x^{2} x 2, so try the other possibilities.
which is what you need. Thus
and you have two numbers (x + 1) and (x  2) whose product is zero. Thus one of them must be zero. That is
or
Penny 

