Using synthetic division, find the quotient q(x) and the remainder r if the polynomial p(x) = x3 − 2x2 − 3x + 18 is divided by (x + 2).

quotient: x^2 - 4x + 5
remainder: 8

Explanation:

1) Given

p(x) = x^3 - 2x^2 - 3x + 18
divisor: x + 2

2) Write the coefficients of p(x) in order:

1       -2        -3      18

3) dividing by x + 2 => run the division  for x = - 2

4) division

     | 1     -2     -3     +18
     |
 -2 |       -2     +8     - 10

      1     -4     +5      +8

The last digit is the remainder, the others are the coefficients of the quotient:

=>

quotient = x^2 - 4x + 5
remainder = 8