Algebra II help

Question

Is (x + 2) a factor of x4 - 3x - 5?

 

Please explain

 

I have to show work using synthetic division 

Answer 1

Hi Maria,

 

Set (x+2) = 0 and you will get x = -2.  To use synthetic division, you must use the -2 for this particular problem.

 

Remember, you must include every power: 1x⁴ + 0x³ + 0x² -3x -5

 

-2   |   1   0   0   -3   -5

              -2   4   -8   22

---------------------------------

          1  -2   4   -11| 17

 

If it happens to be a factor, it should come out to be zero at the end.  In this case, it is not zero.  Therefore, (x+2) is not a factor for x⁴-3x-5.

 

I hope you understood.  Good luck to you.