Question

use synthetic division to find the quotient.
$\frac{2x^{4}+x - 6}{x - 1}$
$?x^{3}+x^{2}+x++\frac{}{x - 1}$

Explanation:

Step1: Identify divisor root

Root of $x-1=0$ is $x=1$.
Coefficients of dividend: $2, 0, 0, 1, -6$ (include 0s for missing $x^3,x^2$ terms)

Step2: Bring down leading coefficient

Bring down $2$ as first quotient term.

Step3: Multiply and add (1st cycle)

Multiply $2$ by $1$: $2\times1=2$. Add to next coefficient: $0+2=2$.

Step4: Multiply and add (2nd cycle)

Multiply $2$ by $1$: $2\times1=2$. Add to next coefficient: $0+2=2$.

Step5: Multiply and add (3rd cycle)

Multiply $2$ by $1$: $2\times1=2$. Add to next coefficient: $1+2=3$.

Step6: Multiply and add (4th cycle)

Multiply $3$ by $1$: $3\times1=3$. Add to last coefficient: $-6+3=-3$. This is the remainder.

Answer:

$2x^3 + 2x^2 + 2x + 3 + \frac{-3}{x-1}$