Remainder Theorem Calculator

The rest theorem calculator is loose on line tool that helps you to calculate the remainder of given polynomial expressions through the rest theorem.

Our aspect theorem calculator offers little by little calculations of the aspect of division. right here you can apprehend a way to locate the the rest of a polynomial the use of the formulation.

What is the the rest Theorem?

In algebra, the remainder theorem or little Bezout’s theorem is an utility of Euclidean division of different expressions, that is located by way of Etienne Bezout. It states when an expression is split via a element x-j, then the the rest of the division is same to f(j).

How to discover Remainders with out Calculator

when the polynomial f(x) is divisible by using a linear issue of the form x-j, the theorem will be utilized by the remainder theorem calculator. if you want to do those calculations by hand, then comply with the instructions beneath and use them to resolve the rest of the polynomial expression in a few minutes.

• The polynomial f(x) is used because the dividend, and the linear expression is used as the divisor.
• The form of the linear expression need to be x-j.
• Then, the remaining value of the polynomial will become m(x).
• consequently, insert the cost of c into the polynomial and compare it to attain the the rest cost.

Example

Solve \( (x^4 + 8x^3 - 6x^2 + 5x - 11) \) with denominator \( (x + 2) \) using the remainder theorem.

Solution: Given values are

$$f(x) = x^4 + 8x^3 - 6x^2 + 5x - 11$$

Since \( x + 2 \) is in the form of \( x - (-2) \),

Then \( c = -2 \)

$$f(-2) = (-2)^4 + 8(-2)^3 - 6(-2)^2 + 5(-2) - 11$$

$$= 16 + 8(-8) - 6(4) + 5(-2) - 11$$

$$= 16 - 64 - 24 - 10 - 11$$

$$= -93$$

The remainder of the given expression is \( -93 \).

How remainder Theorem Calculator Works?

Input:

• First, enter the numerator polynomial.
• Then, replacement the denominator polynomial.
• Hit the “Calculate” button to see the the rest of the given expression.

Output:

The the rest calculator calculates:

• The the rest theorem calculator shows preferred input and the outcomes.
• It provides all steps of the remainder theorem and substitutes the denominator polynomial in the given expression.
• you can locate the remainder regularly by way of clicking at the “Recalculate” button.