SAT Math Practice Question #921 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #921

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

The polynomial function \( P \) is defined by: \[ P(x) = 3x^3 - 4x^2 + cx - 18 \] where the variable coefficient is a constant. When \( P(x) \) is divided by \( (x - 2) \), the remainder is 0. What is the value of the unknown coefficient?
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Socratic AI Engine Step-by-Step Derivation
0ms Precomputed
Tactical Insight (Hint 1)

Recall the Remainder Theorem: if a polynomial \( P(x) \) is divided by \( (x - c) \), the remainder is simply \( P(c) \).

Elimination Framework (Hint 2)

Desmos Shortcut: Enter the polynomial with a slider for the variable. In the next line, evaluate \( P(2) \) and adjust the slider until it equals 0.

Masterclass Solution & Distractor Trap Analysis

By the Polynomial Remainder Theorem, dividing \( P(x) \) by \( (x - c) \) results in a remainder equal to \( P(c) \). Here, \( c = 2 \) and \( P(2) = 0 \). Substitute \( x = 2 \) into \( P(x) \) and equate to 0 to solve for the missing cons...

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

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