If $x+1$ is a factor of $ax^4 + bx^2 + c$, find the value of $a + b + c$? I know that it is equal to zero, but I have to know How to do it.
- Anybody can ask a question
- Anybody can answer
- The best answers are voted up and rise to the top
All you need here is the following fact:
If $(x-r)$ is a factor of the polynomial $P(x)$, then $P(r) = 0$.
Hint: Try dividing $ax^4+bx^2+c$ by $x+1$ through long division. What is the remainder? What should it be?
If you are familiar with synthetic division, you can use that technique to divide $ax^4 + bx^2 + c$ by $x+1$ and find the remainder. Otherwise, you could use long division.
Regardless of what technique you use, for $x+1$ to cleanly divide $ax^4 + bx^2 + c$, then the remainder must be zero. Once you find the remainder, assign values to $a, b, c$ in order to make that remainder zero.
EDIT: Leaving this here as an alternate solution. TonyK's approach is far superior.