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Oplossing - Polynomial division

Eindresultaat Stappen Begrippen en onderwerpen

x^{2} + x + 1

x^2+x+1

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Stapsgewijze uitleg

1. Read dividend and divisor

$(x^{3} - 1) / (x - 1)$

Parse the dividend and divisor polynomials and normalize their terms for long division.

$(x^{3} - 1) / (x - 1)$

Parse the dividend and divisor polynomials and normalize their terms for long division.

$x^{3} - 1$

Parse the dividend and divisor polynomials and normalize their terms for long division.

$x - 1$

Parse the dividend and divisor polynomials and normalize their terms for long division.

$(x^{3} - 1) / (x - 1)$

Parse the dividend and divisor polynomials and normalize their terms for long division.

$(x^{3} - 1) / (x - 1)$

Parse the dividend and divisor polynomials and normalize their terms for long division.

2. Perform polynomial division

$(x^{3} - 1) / (x - 1)$

Apply divide, multiply, and subtract cycles to compute quotient and remainder.

$(x^{3} - 1) / (x - 1)$

Apply divide, multiply, and subtract cycles to compute quotient and remainder.

$(x^{3} - 1) / (x - 1) (c y c l e 1)$

$x^{3} / (x) = x^{2}$

$(x - 1) \cdot (x^{2}) = x^{3} - x^{2}$

Apply divide, multiply, and subtract cycles to compute quotient and remainder.

$x^{3} - x^{2}$

$x^{3} - 1 - (x^{3} - x^{2}) = x^{2} - 1$

Apply divide, multiply, and subtract cycles to compute quotient and remainder.

$x^{2} - 1$

Apply divide, multiply, and subtract cycles to compute quotient and remainder.

$(x^{3} - 1) / (x - 1) (c y c l e 2)$

$x^{2} / (x) = x$

$(x - 1) \cdot (x) = x^{2} - x$

Apply divide, multiply, and subtract cycles to compute quotient and remainder.

$x^{2} - x$

$x^{2} - 1 - (x^{2} - x) = x - 1$

Apply divide, multiply, and subtract cycles to compute quotient and remainder.

$x - 1$

Apply divide, multiply, and subtract cycles to compute quotient and remainder.

$(x^{3} - 1) / (x - 1) (c y c l e 3)$

$x / (x) = 1$

$(x - 1) \cdot (1) = x - 1$

Apply divide, multiply, and subtract cycles to compute quotient and remainder.

$x - 1$

$x - 1 - (x - 1) = 0$

Apply divide, multiply, and subtract cycles to compute quotient and remainder.

$0$

$(x^{3} - 1) / (x - 1) = x^{2} + x + 1$

Apply divide, multiply, and subtract cycles to compute quotient and remainder.

$x^{2} + x + 1$

Apply divide, multiply, and subtract cycles to compute quotient and remainder.

3. Write final form

$(x^{3} - 1) / (x - 1) = x^{2} + x + 1$

$x^{3} - 1 = (x - 1) \cdot (x^{2} + x + 1) + (0)$

$x^{3} - 1 = (x - 1) \cdot (x^{2} + x + 1) + (0)$

Return the quotient and, when needed, add remainder divided by the divisor.

$x^{2} + x + 1$

Return the quotient and, when needed, add remainder divided by the divisor.

$x^{2} + x + 1$

Return the quotient and, when needed, add remainder divided by the divisor.

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Polynoomdeling ondersteunt algebraische vereenvoudiging, factorwerk en rationale uitdrukkingen.

Begrippen en onderwerpen

Polynomial division