1. The problem involves using the Remainder and Factor Theorems to analyze the polynomial $P(x)$ given by values at certain points. 2. The Factor Theorem states that if $(x - a)$ is a factor of $P(x)$, then $P(a) = 0$. 3. The Remainder Theorem states that the remainder when $P(x)$ is divided by $(x - a)$ is $P(a)$. 4. From the table, $P(-1) = 0$ and $P(2) = 0$, so $(x + 1)$ and $(x - 2)$ are factors of $P(x)$ (this matches Tyrone's factors). 5. To check if $(x - 6)$ is a factor (Nia's factor), evaluate $P(6)$. Since $P(6)$ is not given, we cannot confirm this factor from the data. 6. Summary: $(x + 1)$ and $(x - 2)$ are factors because $P(-1) = 0$ and $P(2) = 0$. $(x - 6)$ is not confirmed as a factor without $P(6)$. Final answer: $(x + 1)$ and $(x - 2)$ are factors of $P(x)$; $(x - 6)$ is not confirmed.