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Use the Remainder Theorem to find the remainder when P(x) = x4 – 9x3 – 5x2 – 3x + 4 is divided by x + 3 .
To find the remainder when \(P(x) = x^4 - 9x^3 - 5x^2 - 3x + 4\) is divided by \(x + 3\), we can use the Remainder Theorem.
The Remainder Theorem states that if a polynomial P(x) is divided by x - c, then the remainder is P(c).
In this case, we want to evaluate P(-3) to find the remainder. So we substitute x = -3 into the polynomial:
\[P(-3) = (-3)^4 - 9(-3)^3 - 5(-3)^2 - 3(-3) + 4\]
\[P(-3) = 81 + 81 - 45 + 9 + 4\]
\[P(-3) = 130\]
Therefore, the remainder when \(P(x) = x^4 - 9x^3 - 5x^2 - 3x + 4\) is divided by \(x + 3\) is 130.