Summary :

The calculator allows to find online the quotient and the remainder in the euclidean division of two polynomials or two integers.

Description :

Quotient and Remainder Calculator

The calculator allows to do the euclidean division of polynomials online and the euclidean division of two integers online.

Euclidean division of two polynomials

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 quotient and remainder calculator with the calculator, simply enter polynomials and to apply the euclidean_division function. Thus, for the quotient and remainder calculator 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.

Euclidean division of two integers

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 quotient and remainder calculator with the calculator, simply enter the two integers and apply it to function euclidean_division. Thus, for the quotient and remainder calculator 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.

Syntax :

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

Examples :

• 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}

• 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.
• Quotient and remainder calculator : euclidean_division. The calculator allows to find online the quotient and the remainder in the euclidean division of two polynomials or two integers.
• Pythagorean theorem calculator : pythagorean. The calculator uses the Pythagorean theorem to verify that a triangle is right-angled or to find the length of one side of a right-angled triangle.
• Solve for x calculator : equation_solver. The equation solver allows to solve equations with an unknown with calculation steps : linear equation, quadratic equation, logarithmic equation, differential equation.
• Valuation of a polynomial : valuation. The valuation function allows to calculate the valuation of a polynomial online.