SAT Math Practice Question #558 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #558

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

Let \( p(x) = x^3 + ax^2 + bx + c \), where \( a \), \( b \), and \( c \) are constants. When \( p(x) \) is divided by \( x - 2 \), the remainder is \( 15 \). When \( p(x) \) is divided by \( x + 1 \), the remainder is \( -6 \). If \( x - 1 \) is a factor of \( p(x) \), what is the value of \( p(3) \)?
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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 rigorous test of the Polynomial Remainder Theorem, which states that when a polynomial \( p(x) \) is divided by \( (x - r) \), the remainder is \( p(r) \). Step 1: Translate the given conditions into equations. Condition 1: Divide...

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

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