SAT Math Practice Question #757 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #757

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

Let \( P(x) = ax^4 + bx^3 + cx^2 + dx + e \), where \( a, b, c, d, \) and \( e \) are constants. When \( P(x) \) is divided by \( (x - 2) \), the remainder is 15. When \( P(x) \) is divided by \( (x + 2) \), the remainder is -9. What is the remainder when \( P(x) \) is divided by \( x^2 - 4 \)?
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Socratic AI Engine Step-by-Step Derivation
0ms Precomputed
Tactical Insight (Hint 1)

Identify the quadratic form: consider converting to vertex form \( y = a(x-h)^2 + k \) or using \( x = - rac{b}{2a} \) to find the line of symmetry.

Elimination Framework (Hint 2)

Elimination Shortcut: Check the extremes or test answer choices starting with C to binary search the correct magnitude.

Masterclass Solution & Distractor Trap Analysis

This is a beautifully complex Polynomial Remainder Theorem question. Let's break it down like a master tutor. First, recall the core rule of the Polynomial Remainder Theorem: When a polynomial \( P(x) \) is divided by \( (x - c) \), the rem...

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

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