Explain algebra of real functions

Dear Student, 
It is simply adding , subtracting , multiplying, dividing polynomial equation. 
 

• Addition: (f + g)(x) = f(x) + g(x)
• Subtraction: (f - g)(x) = f(x) - g(x)
• Multiplication: (f ⋅ g)(x) = f(x) ⋅ g(x)
• Division: (f / g)(x) = f(x) / g(x), where g(x) ≠ 0

Example:
(2x + 5y) + (3x – 2y) 
  =  2x + 5y + 3x – 2y 
  =  2x + 3x + 5y – 2y 
  =  5x + 3y

or 

(4x² - 2x) - (-5x² - 8x)

= 4x² - 2x + 5x² + 8x.

= 4x² + 5x² - 2x + 8x.

= 9x² + 6x.

= 3x(3x + 2)

And


Divide 2x² +3x+1 by x+2
 
and