Assignment:
Note the polynomial form P(x) = x2 - a. And, note that the two linear factors ( x + a ) ( x - a ), when multiplied together, yield ( x + a ) ( x - a ) = x2 - a.
Consequently, we note that an equation of the form
x2 - a= 0
can be factored as
( x + a ) ( x - a ) = 0,
giving the two zeros of our equation
x = a, -a.
For an arbitrary integer a and an equation of the form x2 - a = 0, how would you use the response of DQ 2 to determine if our two zeros are, indeed, integers? Can you exhibit an example?
Provide complete and step by step solution for the question and show calculations and use formulas.