Find the quotient and remainder using synthetic division for?

Question

Fraction: {x^3 + 4 x^2 + 8 x + 16}{x+2}.

Quotient:

remainder:

having trouble with finding the answer

Answer 1

The quotient is x² + 2x + 4.

The remainder is 8.

Remember, the linear divisor is (x - c). Since (x - c) in this case is (x + 2), then c = -2. So -2 is the divisor we want to use in our synthetic division process. Here's how we get the answer:

-2)
1 4 8 16
1 -2 -4 -8
-------------
1 2 4 8


First write your divisor up at the top left corner and mark it off from the coefficients of the terms you will be dividing it into. Now, bring down the coefficient of the leading term and multiply it by the divisor. Place that product under the second coefficient and add them together. Next, multiply the sum of these numbers by the divisor and add that product to the third coefficient. Finally, multiply that sum by the divisor and add that product to the last coefficient. The sum of these last two numbers will give you the remainder. In this particular case, it's 8. Notice that the coefficients of each term are given by sums at the bottom of each column, and the remainder is the rightmost number.