Digital ACT Math Practice Question #2107
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Remainder Theorem shortcut: $P(3) = 19 \implies 2(27) - 45 + 3k - 8 = 19 \implies 3k + 1 = 19 \implies k = 6$.
By the Remainder Theorem, dividing $P(x)$ by $(x - 3)$ gives remainder $P(3)$. $P(3) = 2(3)^3 - 5(3)^2 + 3k - 8 = 2(27) - 5(9) + 3k - 8 = 54 - 45 + 3k - 8 = 3k + 1$. We are given $P(3) = 19 \implies 3k + 1 = 19 \implies 3k = 18 \implies k =...
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