Problem
\( P(x) \) is a polynomial. - \( P(x) \) divided by \( (x-9) \) has a remainder of 1 . - \( P(x) \) divided by \( (x-4) \) has a remainder of 7 . - \( P(x) \) divided by \( (x+4) \) has a remainder of 0 . - \( P(x) \) divided by \( (x+9) \) has a remainder of -5 . Find the following values of \( P(x) \). \[ P(4)= \]
Solution
Step 1 ：\( P(x) = (x-9)Q_1(x) + 1 \)
Step 2 ：\( P(x) = (x-4)Q_2(x) + 7 \)
Step 3 ：\( P(4) = (4-4)Q_2(4) + 7 \)
Step 4 ：\( P(4) = 7 \)
