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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.

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3 Answers 3

All you need here is the following fact:

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

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

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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.

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