We can use synthetic division to divide a polynomial by a linear function.
e.g. 3x3 – 5x + 7 ÷ (x + 2)
-2
3
3
0
-6
-6
Remember to include zero coefficients
-5
7
12 -14
7
-7
Remainder
These are the coefficients of the quadratic
So 3x3 – 5x + 7 ÷ (x + 2) = 3x2 – 6x + 7 remainder (-7)
or 3x3 – 5x + 7 = (3x2 – 6x + 7)(x + 2) – 7