SAT Math Practice Question #260 (Hard (710)) | Test Citadel
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SAT Math Difficulty: Hard (710)

Digital SAT Math Practice Question #260

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

The polynomial \( p(x) = 2x^3 - 5x^2 + ax + b \), where \( a \) and \( b \) are constants, is perfectly divisible by \( (x - 2) \). When \( p(x) \) is divided by \( (x + 1) \), the remainder is \( -9 \). 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

Get ready to use the Polynomial Remainder Theorem! If you haven't mastered this yet, it's a massive cheat code for the SAT. The theorem states that when a polynomial \( p(x) \) is divided by \( (x - c) \), the remainder is exactly equal to ...

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

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