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If the polynomial (x^(3)-3x^(2)+ax+18) i...

If the polynomial `(x^(3)-3x^(2)+ax+18)` is divided by (x-4), the remainder is 58. Find the value of a.

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To solve the problem, we need to find the value of \( a \) such that when the polynomial \( P(x) = x^3 - 3x^2 + ax + 18 \) is divided by \( x - 4 \), the remainder is 58. ### Step-by-Step Solution: 1. **Use the Remainder Theorem**: According to the Remainder Theorem, if a polynomial \( P(x) \) is divided by \( x - c \), the remainder is \( P(c) \). In this case, we will evaluate \( P(4) \). \[ P(4) = 4^3 - 3(4^2) + a(4) + 18 ...
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