Question

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).

Answer 1

Answer:

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

Step-by-step 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