SAT Math Practice Question #578 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #578

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

\[ f(x) = x^{15} - 2x^{14} + ax^3 + bx - 6 \] In the polynomial function \( f \) defined above, \( a \) and \( b \) are constants. When \( f(x) \) is divided by \( (x - 2) \), the remainder is \( 22 \). When \( f(x) \) is divided by \( (x + 1) \), the remainder is \( -14 \). What is the value of \( a \cdot b \)?
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Socratic AI Engine Step-by-Step Derivation
0ms Precomputed
Tactical Insight (Hint 1)

Check for special right triangles (\( 30^\circ-60^\circ-90^\circ \) or \( 45^\circ-45^\circ-90^\circ \)) or the complementary angle identity \( \sin(x) = \cos(90^\circ - x) \).

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 masterpiece of an SAT Math problem. It looks intimidating because of the \( x^{15} \) term, but it is actually a beautiful test of the Polynomial Remainder Theorem combined with a system of linear equations. Step 1: Understand the...

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

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