P ( x )

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!