Answer
$x^2+x+4$; remainder $12$
Work Step by Step
Write the coefficients of the dividend in decreasing degree inside the synthetic division symbol. Determine the value $c$ of the divisor $x-c$.
The division expression has:
$c=2$
coefficients of the dividend in descending degree order: $1, -1, 2, 4$.
Thus, the division problem becomes:
$2)\overline{\text{1 -1 2 4}}$
Perform the synthetic division to obtain:
(refer to the image below)
Therefore, the quotient is:
$x^2+x+4$; remainder $12$
