SAT Math Practice Question #480 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #480

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

The polynomial \( P(x) = ax^3 + bx^2 + cx + d \) has a remainder of \( 5 \) when divided by \( (x - 2) \), and a remainder of \( -3 \) when divided by \( (x + 1) \). If \( P(x) \) is divided by \( x^2 - x - 2 \), the remainder is \( Rx + S \), where \( R \) and \( S \) are constants. What is the value of \( R - S \)?
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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

Are you ready for some elite-level number theory and polynomial division? This question separates the 790s from the 800s. We will combine the Polynomial Remainder Theorem with the Division Algorithm. Step 1: Apply the Polynomial Remainder T...

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

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