SAT Math Practice Question #537 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #537

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

The polynomial \( p(x) = ax^4 - 3x^3 + bx^2 + 4x - 6 \) is divided by \( (x - 2) \), resulting in a remainder of 10. When \( p(x) \) is divided by \( (x + 1) \), the remainder is -17. What is the value of \( a - b \)?
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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 question is a masterclass in the Polynomial Remainder Theorem disguised as a system of linear equations. Let's break down the logic. Step 1: Apply the Remainder Theorem. The Remainder Theorem states that if a polynomial \( p(x) \) is d...

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

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