Answer:
3x² + x - 3
Explanation:
The way I like to do it is to get rid of the x's and just use the numbers in the case of synthetic division
Pretend the square root of the division symbol
-4 √ 3 12 1 -12
Quick note: We're dividing by -4 because we're dividing by x + 4
First bring down the 3
-4 √ 3 13 1 -12
3
Multiply it by 4 then bring add it to the next number
-4 √ 3 13 1 -12
-12
3 1
Add that number to the next one
-4 √ 3 13 1 -12
-12 -4
3 1 -3
Finally repeat the step for the last number
-4 √ 3 13 1 -12
3 -12 -4 +12
3 1 -3 0
Now take those bottom numbers and add back the x's but with one less power, so the starting x³ would now become x², x² would become x, and so on
3x² + 1x - 3