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Remainder Theorem Calculator
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Remainder theorem is the theorem used to factorize the function of the form f(x) where x is a polynomial when it is divided by variable of the form (x - a). Here a is some number. 

Remainder Theorem Calculator
calculates the remainder of the polynomial of any given function when it is divided by any linear factor.

You can see two default polynomials given below. When you click on "Divide", remainder is calculated by dividing the given polynomial function by linear factor.
 

Steps for Remainder Theorem Calculator

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Step 1 :  

Use the synthetic division method to get the expression of the form:

f(x) = (x - a) q(x) + r

Where f(x) = given function,

q(x) = quotient,

r = remainder.



Step 2 :  

Using the Remainder theorem, find solution for x when function f(x) = x2 + 5x + 6 is divided by x + 3.



Problems on Remainder Theorem Calculator

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  1. Given function is f(x) = x2 + 5x + 6 and linear factor = x + 3


    Step 1 :  

    x+3 | $\overline{x^{2} + 5x + 6}$ | x+2


                x2 + 3x


                     $\overline{2x + 6}$


                     $\overline{2x + 6}$


                     $\overline{             0}$



    Step 2 :  

    x2 + 5x + 6 = (x + 2) (x + 3) + 0.

    Remainder = 0 and x = -2 is another solution for x2 + 5x +6.



    Answer  :  

    Using the remainder theorem, find solution for x when function f(x) = x2 + 4x + 6 is divided by x + 2.



  2. Given function is f(x) = x2 + 4x + 6 and linear factor = x + 2


    Step 1 :  

    x+2 | $\overline{x^{2} + 4x + 6}$ | x+2


                x2 + 2x


                     $\overline{2x + 6}$


                     2x + 4


                    $\overline{            2}$



    Step 2 :  

    x2 + 4x + 6 = (x + 2) (x + 2) + 2,
    Remainder = 2 and (x + 2) is the another solution



    Answer  :  

    x2 + 4x + 6 = (x + 2) (x + 2) + 2,
    Remainder = 2 and (x + 2) is the another solution



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