Ruffini's table

Ruffini’s rule makes division by a binomial $(x-c)$ particularly quick: it is enough to work with the coefficients alone, laid out in a table.

Property — Ruffini's table

To divide $a_nx^n+a_{n-1}x^{n-1}+\cdots+a_0$ by $(x-c)$, the coefficients are laid out in a table: the first coefficient is brought down, multiplied by $c$, added to the next coefficient, and so on.

Example

$(6x^3 - 2x + 4) \div (x-2)$. Warning: the coefficient of $x^2$ is $0$ and must be written.

	$x^3$	$x^2$	$x$	$1$
Coefficients	$6$	$0$	$-2$	$4$
$c=2$		$12$	$24$	$44$
Result	$6$	$12$	$22$	$\boxed{48}$
Meaning	$x^2$	$x$	$1$	$R$

Quotient: $6x^2+12x+22$; remainder: $48$.

Links

Topics: Algebraic calculation
Concepts: Division between polynomials · Ruffini’s rule
Skills: Calculating
People: Paolo Ruffini