SAT Math Practice Question #398 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #398

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

Let \( P(x) = x^4 + ax^3 - 7x^2 + bx - 12 \), where \( a \) and \( b \) are constants. When \( P(x) \) is divided by \( (x - 2) \), the remainder is \( -18 \). When \( P(x) \) is divided by \( (x + 3) \), the remainder is \( -33 \). 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

The key to unlocking this question is the Polynomial Remainder Theorem. The Remainder Theorem states that if you divide a polynomial \( P(x) \) by \( (x - c) \), the remainder is simply the value of \( P(c) \). **Step 1: Set up the first eq...

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

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