SOLUTION: If someone could please help me with this, it will be greatly appreciated! If x + 1 is a factor of ax^4 + bx^2 + c, what is the value of a + b + c? My work so far before g

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: If someone could please help me with this, it will be greatly appreciated! If x + 1 is a factor of ax^4 + bx^2 + c, what is the value of a + b + c? My work so far before g      Log On


   

Question 848809: If someone could please help me with this, it will be greatly appreciated!
If x + 1 is a factor of ax^4 + bx^2 + c, what is the value of a + b + c?
My work so far before getting stuck:
I was trying to use Synthetic division, but evidently it didn't work out as I had hoped:
-1 ˩.a..b..І..c
.......Ab..І.ab-b
.....a.ab-bІ.1
1=c-ab-b

1=c-ab-b
Answer by fcabanski(1391) About Me  (Show Source):
You can put this solution on YOUR website!
When you perform the synthetic division, remember the coefficients of x^3 and x. Both are 0. That will lead to the correct answer. The final factor has to be = to 0. It will be a+b+c.


The other way to solve this is:


If x+1 is a factor of the polynomial p(x), x=-1 and p(-1) = 0 according to the remainder theorem.


Set p(-1) = 0. Then solve for a+b+c


ax%5E4+%2B+bx%5E2+%2B+c+=+0

+a%28-1%29%5E4+%2B+b%28-1%29%5E2+%2B+c+=+0


a+b+c = 0