Question 54473
:
(x^3 - ax^2 + 7x + 10). Find a if (x+2) is a factor
:
You can use synthetic division, looking for a remainder of 0:
Used "..." to try and get it to line up, without much success
:
...._______________________
 -2 | 1 - a   +   7   +    10
...........- 2 + (2a+4)  + (-4a-22)
......---------------------------
.........1 + (-a-2) + (2a+11) + 0
:
10 + (-4a - 22) = 0 
-4a - 22 + 10 = 0
     -4a - 12 = 0
          -4a = +12
            a = +12/-4
            a = -3

That would give you x^3 - (-3)x^2 + 7x + 10
Which is; x^3 + 3x^2 + 7x + 10
:
Divide (x+2) into this and you get: x^2 + x + 5