Question

use synthetic division to show that x+3 is a factor of x^3+3x^2+4x+12

Answer 1

you don't need it... you can use the factor theorem

f(-3) = (-3)^3 + 3(-3)^2 + 4(-3) + 12

f(-3) = 0 therefore a factor

Answer 2

1 3 4 12
0 -3 0 -12
1 0 4 0
remainder is therefore 0