Given 
P
(
x
)
P(x)​ below, evaluate 
P
(
3
)
P(3)​.

P
(
x
)
=
(
x
−
2
)
(
x
+
8
)
(
x
−
3
)
(
x
+
7
)
P(x)=(x−2)(x+8)(x−3)(x+7)

To evaluate \( P(3) \) given the polynomial:

\[
P(x) = (x - 2)(x + 8)(x - 3)(x + 7)
\]

we substitute \( x = 3 \) into the equation:

\[
P(3) = (3 - 2)(3 + 8)(3 - 3)(3 + 7)
\]

Now, simplify each factor:

\[
P(3) = (1)(11)(0)(10)
\]

Since one of the factors is 0, the entire product will be 0:

\[
P(3) = 0
\]

Thus, \( P(3) = 0 \).

Would you like any further explanation or details on how this was done?

### Related Questions:
1. How would you find the zeros of \( P(x) \)?
2. What is the degree of the polynomial \( P(x) \)?
3. How do you factor a polynomial like \( P(x) \)?
4. Can you expand the polynomial \( P(x) \)?
5. What is the relationship between the roots and the factors of a polynomial?

#### Tip:
Always check for a zero factor when evaluating a product of terms—if one term is zero, the entire expression simplifies quickly!

Given P(x) below, evaluate P(3). P(x) = (x - 2)(x + 8)(x - 3)(x + 7)

Learn how to evaluate the polynomial P(x) = (x - 2)(x + 8)(x - 3)(x + 7) at x = 3. This step-by-step solution covers key algebraic concepts such as polynomial factorization and the Zero Product Property. Suitable for students in Grades 9-10.

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