SAT Math Practice Question #457 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #457

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

The polynomial \( P(x) = x^4 + ax^3 + bx^2 + cx + d \) has strictly real coefficients. It is given that \( P(1 + i) = 0 \) and \( P(2) = 0 \). When \( P(x) \) is divided by \( x + 1 \), the remainder is \(-30\). What is the value of \( d \)?
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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 question is an absolute masterclass in polynomial theorems! You have to tie together the Complex Conjugate Root Theorem, the Factor Theorem, and the Remainder Theorem. Step 1: Identify the roots. The polynomial has degree 4, meaning it...

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

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