SOLUTION: Determine the value of 'a' if (x + 2) is a factor of (x³ - ax² + 7x + 10). Many thanks

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Question 54473: Determine the value of 'a' if (x + 2) is a factor of
(x³ - ax² + 7x + 10).
Many thanks
Found 2 solutions by ankor@dixie-net.com, Edwin McCravy:
Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
:
(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
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
Determine the value of 'a' if (x + 2) is a factor of 
(x³ - ax² + 7x + 10). 

Plan
1. Divide x³ - ax² + 7x + 10 synthetically by x + 2
2. Set remainder = 0
3. Solve for "a".

1.

     -2|1    -a       7      10
       |     -2    2a+4  -4a-22   
        1  -a-2   2a+11  -4a-12  

2. This remainder, -4a-12, must equal 0 in order that
   (x + 2) be a factor, so

        -4a - 12 =  0
3.           -4a = 12
               a = -3

Edwin McCravy
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