SAT Math Practice Question #366 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #366

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

The polynomial function \( p \) is defined by \( p(x) = x^4 - 2x^3 + cx^2 + dx - 15 \), where \( c \) and \( d \) are constants. When \( p(x) \) is divided by \( x^2 + 3 \), the remainder is \( 0 \). What is the value of \( c + d \)?
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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 is an elite-level algebra problem that tests your understanding of the Polynomial Remainder Theorem combined with complex numbers (or polynomial long division). Let's walk through the most elegant way to solve it. If dividing \( p(x) \...

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

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