find the number a such that x + 2 is a factor of 4x^3 + ax^2 -5x - 2

synthetic division leads us to the terms
4
a-8
11-2a
4a-24
so 4a-24=0 leads to a=6

Divide (x^3+2x^2-3x+2) / (x+1)

synthetically we get coefficients: 1, 1, -4 with remainder 6. 

i.e. 

Divide using long division and synthetic division f(x)=(6x^3+17x^2+27x+20)÷(3x+3)

-1|
------
6        |6
17   -6|11
27  -11|16
20 -16|4 


 

Divide check your answer if there is a remainder write the remainder over the divisor. (y^3-y^2-31y+2) / (y+5)

5| 1 -1 -31 2
|
-5 30 5 
_______________
1 -6 -1 R7

Divide -3x^3 - 2x^2 - x - 2 by x – 2. A. -3x2 + 4x + 15, R 32, B. -3x2 + 4x + 15, C. -3x2 - 8x - 17, D. -3x2 - 8x - 17, R –36

D: 

2|-3 -2 -1 -2
| 
|      -6  -16 -34
___________ 
  -3 -8 -17    R -36