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
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
