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 \( P(x) \).
\[
P(4)=
\]

Answer

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Answer

\( P(4) = 7 \)

Steps

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 ：\( P(4) = 7 \)

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