ACT Math Practice Question #2107 (Hard) | Test Citadel
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ACT Math Difficulty: Hard

Digital ACT Math Practice Question #2107

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When the polynomial $P(x) = 2x^3 - 5x^2 + kx - 8$ is divided by $(x - 3)$, the remainder is 19. What is the value of the constant $k$?
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Remainder Theorem shortcut: $P(3) = 19 \implies 2(27) - 45 + 3k - 8 = 19 \implies 3k + 1 = 19 \implies k = 6$.

Masterclass Solution & Distractor Trap Analysis

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 =...

Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...

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