ACT Math Practice Question #1208 (Hard (33)) | Test Citadel
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ACT Math Difficulty: Hard (33)

Digital ACT Math Practice Question #1208

Test your problem-solving accuracy on this official-caliber item. Select an answer choice to check your reasoning instantly.

What is the remainder when the polynomial $P(x) = 2x^4 - 5x^3 + 3x - 7$ is divided by $(x - 2)$?
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Socratic AI Engine Step-by-Step Derivation
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⚡ 15-Second Desmos Speed Hack

Never do long division on the ACT! Plug $x = 2$ directly into the polynomial: $32 - 40 + 6 - 7 = -9$.

Masterclass Solution & Distractor Trap Analysis

According to the Polynomial Remainder Theorem, the remainder of a polynomial $P(x)$ divided by $(x - c)$ is simply $P(c)$. Here, $c = 2$. $$P(2) = 2(2)^4 - 5(2)^3 + 3(2) - 7 = 2(16) - 5(8) + 6 - 7 = 32 - 40 + 6 - 7 = -8 + 6 - 7 = -9.$$...

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

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