SAT Math Practice Question #526 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #526

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

Let \( P(x) = x^4 + ax^3 + bx^2 + cx + d \) be a polynomial, where \( a \), \( b \), \( c \), and \( d \) are constants. The polynomial \( P(x) \) is perfectly divisible by both \( (x - 2)^2 \) and \( (x + 1)^2 \). What is the value of \( a + b + c + d \)?
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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 a brilliantly deceptive question. At first glance, you might think you need to expand \( (x - 2)^2 (x + 1)^2 \) into a degree-4 polynomial, match the coefficients to \( a, b, c, \) and \( d \), and then add them all together. While ...

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

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