Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.

share|cite|improve this question

All you need here is the following fact:

If $(x-r)$ is a factor of the polynomial $P(x)$, then $P(r) = 0$.

share|cite|improve this answer

Hint: Try dividing $ax^4+bx^2+c$ by $x+1$ through long division. What is the remainder? What should it be?

share|cite|improve this answer

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.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.