ividing the polynomial $$ P(x) $$ by $$ x-5 $$ yields a quotient $$ Q(x) $$ and a remainder of 2 . If $$ Q(-5)=-5 $$, find $$ P(-5) $$ and $$ P(5) $$ $$ P(-5)= $$ $$ P(5)=\square $$

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We are given that
$$
P(x) = (x-5)Q(x) + 2.
$$

1. To find $$ P(5) $$, substitute $$ x = 5 $$:
   $$
   P(5) = (5-5)Q(5) + 2 = 0 \cdot Q(5) + 2 = 2.
   $$

2. To find $$ P(-5) $$, substitute $$ x = -5 $$:
   $$
   P(-5) = (-5-5)Q(-5) + 2 = (-10)Q(-5) + 2.
   $$
   Given $$ Q(-5) = -5 $$, we have
   $$
   P(-5) = (-10)(-5) + 2 = 50 + 2 = 52.
   $$

Thus:
$$
P(-5) = 52 \quad \text{and} \quad P(5) = 2.
$$
$$ P(-5) = 52 $$ and $$ P(5) = 2 $$.

ividing the polynomial by yields a quotient and a remainder of 2 . If , find and

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