Question

Polynomial division (d^2 + 8d + 12)/(d + 2)

Answer 1

We want to perform the following division:

$\frac{d^2+8d+12}{d+2}$

First, we rewrite the numerator and denominator as follows:

$d^2+8d+12|d+2$

Then, we divide the term of greatest degree of the numerator by the term of greatest degree of the denominator and write the result bellow the denominator:

d² + 8d + 12 | d + 2

d

Now we subtract from the numerator the product of this division and the denominator:

d² + 8d + 12 | d + 2

-d² - 2d | d

6d + 12

Now we reproduce the same steps again with this result

Setep 1:

d² + 8d + 12 | d + 2

-d² - 2d | d

6d + 12 | d + 2

d + 6

Step 2:

d² + 8d + 12 | d + 2

-d² - 2d | d

6d + 12 | d + 2

-6d - 12 | d + 6

0

Since this division has no rest, the answer is given by:

$\frac{d^2+8d+12}{d+2}=d+6$