- Inicio
- Polynomials
- Ruffini's rule
- Ejercicios
Ruffini's rule
Do the division $\dfrac{p(x)}{q(x)}$, where $p(x)=-x^4+ax^3-3x^2+2x-3$ and $q(x)=x-2$, and impose the value of the parameter $a$ so that the division has a remainder equal to $3$.
We apply Ruffini's rule:
| $-1$ | $+a$ | $-3$ | $+2$ | $-3$ | |
| $2$ | $-2$ | $2(a-2)$ | $2(2(a-2)-3)$ | $2(2(2(a-2)-3)+2)$ | |
| $-1$ | $a-2$ | $2(a-2)-3$ | $2(2(a-2)-3)+2$ | $2(2(2(a-2)-3)+2)-3$ |
Therefore, now we have to solve the following equation:
$$2(2(2(a-2)-3)+2)-3=3$$
So:
$$2(2(2(a-2)-3)+2)-3=3 \Leftrightarrow 2(2(2(a-2)-3)+2)=0 \Leftrightarrow$$
$$2(2(a-2)-3)+2=0 \Leftrightarrow 2(2(a-2)-3)=-2 \Leftrightarrow$$
$$2(a-2)-3=-1 \Leftrightarrow 2(a-2)=2 \Leftrightarrow a=3$$
With the value of $a=3$, the result of the division has a remainder equal to $3$.