Two polynomials P and D are given.

Question

Use either synthetic or long division to divide P(x) by  D(x), and express the quotient  P(x)/D(x) in the form P(x)D(x)= Q(x) + R(x)/D(x).

 

P(x) = 2x³ + 4x² − 2x − 1, D(x) = x + 3

 

P(x)/D(x)=

Answer 1

Use synthetic division.  It will be faster and more efficient.

 

Divide the coefficients of P(x) by the possible of P(x). 

 

-3 | 2       4          -2           -1

 

              -6           6           -12

__________________________

      2      -2           4           -13

 

 

Q(x) = 2x² - 2x + 4

R(x) = -13

 

 

Now put all the information into the required form.

 

P(x) / D(x) = (2x² - 2x + 4) - [13 / (x + 3)]

Answer 2

-3 | 2 4 -2 -1
-6 6 -12
------------------------------
2 -2 4 -13



(x + 3)( 2x^2 - 2x + 4) - 13 =

2x^3 - 2x^2 +4x + 6x^2 - 6x + 12 - 13 =

2x^3 + 4x^2 - 2x - 1

 

The polynomial in mixed number format:
(2x^2 - 2x) + 4 - 13/(x+1)