The problem extracted from the image is:

6. If $(x - 1)$ is a factor of the polynomial $P(x)$, write $P(1)$.

Solution:

By the Factor Theorem, if $(x - c)$ is a factor of $P(x)$, then $P(c) = 0$.

Here, $(x - 1)$ is a factor of $P(x)$, so: $P(1) = 0$

Final Answer:

$P(1) = 0$

Would you like a more detailed explanation or examples of the Factor Theorem?

Related Questions:

1. What is the Factor Theorem, and how does it relate to polynomial division?
2. If $P(x) = x^3 - 3x^2 + 3x - 1$, verify that $x - 1$ is a factor.
3. How can we use synthetic division to confirm if $(x - 1)$ is a factor of a polynomial?
4. Explain the relationship between the roots of a polynomial and its factors.
5. How do we construct a polynomial if we are given its factors?

Tip:

Always test roots by substituting them into the polynomial using the Factor Theorem to verify whether they are factors.