I found the answers to the following question using long division but I was supposed to use synthetic division. The thing is I don't understand how to do synthetic division. Can someone help me??

1. (x2 + 13x + 40) ÷ (x + 8).
2. (2x2 – 23x + 63) ÷ (x – 7).
3. Let f(x) = 4x3 + 7x2 – 13x – 3 and g(x) = x + 3. Find f(x)/g(x).
4. Let f(x) = 3x3 – 4x – 1 and g(x) = x + 1. Find f(x)/g(x).

Question

I found the answers to the following question using long division but I was supposed to use synthetic division. The thing is I don't understand how to do synthetic division. Can someone help me??

1. (x2 + 13x + 40) ÷ (x + 8).
2. (2x2 – 23x + 63) ÷ (x – 7).
3. Let f(x) = 4x3 + 7x2 – 13x – 3 and g(x) = x + 3. Find f(x)/g(x).
4. Let f(x) = 3x3 – 4x – 1 and g(x) = x + 1. Find f(x)/g(x).

anonymous · Answer

These are the answers i have for them.
$$1.~~x+5$$
$$2.~~2x-9$$
$$3.~~4x^2 - 5x - 9/x + 3 + 2 $$ 
$$4.~~3x^2-3x-1$$

phi · Answer

see http://www.khanacademy.org/math/algebra/polynomials/dividing_polynomials/v/synthetic-division

phi · Answer

For division by higher order polynomials see https://en.wikipedia.org/wiki/Synthetic_division#Expanded_synthetic_division for a leading coefficient ≠ 1, scroll down to https://en.wikipedia.org/wiki/Synthetic_division#For_non-monic_divisors