The euclidean_division function to calculate online the quotient and the remainder in the euclidean division of two polynomials or two integers.

euclidean_division online

The calculator with the **euclidean_division** function allows to do the
euclidean division of polynomials
**online**. As a calculator, **euclidean_division** also allows to do
the euclidean division of two integers **online**.

A and B are two **polynomials**, to do **euclidean** **division** of A by B returns
to find polynomials Q and R such that A=BQ+R with degree R< degree B. If R=0, we say that B divides A.
This is sometimes called division shall descending powers.

To perform the euclidean division with the calculator, simply enter polynomials and to apply the
euclidean_division function. Thus, for the **euclidean division of polynomials **
such as the following : `1+x+x^2` et `x`, enter euclidean_division(x^2+x+1;x) or directly x^2+x+1;x,
if the button euclidean_division already appears, the result `{x^2+x+1=x*(1+x)+1}` is returned. The **quotient**
of the Euclidian division is 1+x and the **remainder** is equal to 1.

a and b are two **integers**, to do **euclidean** **division** of a by b returns to find
integers q et r such that a = bq+r with r < b. If r = 0, we say that b divides a.

To perform the euclidean division with the calculator, simply enter the two integers and apply it to
function euclidean_division. Thus, for the **euclidean division of two integers**
such as the following : 19 et 3, you must enter euclidean_division(19;3) or directly 19;3,
if the euclidean_division already appears, the result `{19=3*6+1}` is returned. The **quotient** is equal to
6 and the **remainder** of the euclidean division is 1.

The euclidean_division function to calculate online the quotient and the remainder in the euclidean division of two polynomials or two integers.

- For polynomials divisions
- euclidean_division(polynomial;polynomial) or
- euclidean_division(polynomial/polynomial)
- For integers divisions
- euclidean_division(integer;integer) or
- euclidean_division(integer/integer)

- euclidean_division(`x^2+x+1;x`) returns `{x^2+x+1=x*(1+x)+1}`
- euclidean_division(`(x^2+x+1)/x`) returns `{x^2+x+1=x*(1+x)+1}`
- euclidean_division(`19;3`) returns {19=3*6+1}
- euclidean_division(`19/3`) returns {19=3*6+1}

See also

- Degree of a polynomial : degree. The degree function calculates online the degree of a polynomial.
- Calculation of the discriminant online : discriminant. Calculator that allows the calculation of the discriminant of a quadratic equation online.
- Equation solver : equation_solver. The equation solver allows to solve equations with an unknown with calculation steps : linear equation, quadratic equation, logarithmic equation, differential equation.
- Euclidean division : euclidean_division. The euclidean_division function to calculate online the quotient and the remainder in the euclidean division of two polynomials or two integers.
- Pythagorean theorem : pythagorean. The function makes it possible to verify by using the Pythagorean theorem knowing the lengths of the sides of a triangle that this is a right triangle. If the sides of the triangle depend on a variable, then the value of the variable is calculated so that the triangle is a right triangle.
- Valuation of a polynomial : valuation. The valuation function allows to calculate the valuation of a polynomial online.