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State True or False. If $$\frac{x^4 + x^2 + 1}{x^2 + x + 1} = px^2 + qx + r$$ then $$p + q + r = 1$$
Correct Answer: True
$$x^4 + x^2 + 1 = (x^2 + x + 1)(x^2 - x + 1)$$, so the quotient is $$x^2 - x + 1$$. Then $$p = 1$$, $$q = -1$$, $$r = 1$$ and $$p + q + r = 1$$. The statement is True.
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