divide using synthetic division
(5x^4+12x^3-21x^2-40x-12) divide (x+3)
To divide using synthetic division, we need to set up the equation in the form (x+3) = 0.
So, x + 3 = 0
x = -3
Now, we write the coefficients of the dividend: 5x^4 + 12x^3 - 21x^2 - 40x - 12 as:
5 12 -21 -40 -12
Then, we use synthetic division:
-3 | 5 12 -21 -40 -12
| -15 -81 186 -132
_____________________________
5 -3 105 -174 -144
Therefore, the quotient is 5x^3 - 3x^2 + 105x - 174, and the remainder is -144.