Advanced Functions - Remainder Theorem

The remainder theorem says that if a function (f(x)) is divided by (x – a), the remainder is f(a). Meaning that if you use the value for division as a value of “x” for the function, the value of the division of (f(x)/a) is the result.


Therefore f(x)/a is equal to f(a).


One of the applications of this is that if a value is a factor, then the remainder should be zero (0). Therefore, it is possible to check if a value is a factor of a function by substituting the value into the function and checking if the result ends up as 0.


Quotient Form and Corresponding Statement


Quotient form and corresponding statement are simply different ways of writing the equation with its remainder.


In quotient form, the original function is written, and then it equals the original function multiplied by the divisor, plus the remainder.




The corresponding statement begins with the original function divided by the divisor, then it equals the original function plus the remainder divided by the divisor.




Synthetic Division


Synthetic division is an easier way to divide a polynomial by a value and find the remainder. This is also useful for dividing a polynomial by one of it’s factors to simplify and factor fully.





If you have any questions, leave them in the comments below.