SAT Math Practice Question #277 (Hard (740)) | Test Citadel
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SAT Math Difficulty: Hard (740)

Digital SAT Math Practice Question #277

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

Let \( P(x) = ax^3 + bx^2 - 14x + 8 \), where \( a \) and \( b \) are constants. If \( P(x) \) is divisible by both \( (x - 2) \) and \( (x + 1) \), what is the value of \( a + b \)?
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Socratic AI Engine Step-by-Step Derivation
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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 beautiful high-level polynomial question that combines the Factor Theorem with systems of equations. Let's break it down. Step 1: Understand the Factor Theorem. The Factor Theorem states that if a polynomial \( P(x) \) is divisibl...

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

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