SAT Math Practice Question #291 (Hard (770)) | Test Citadel
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SAT Math Difficulty: Hard (770)

Digital SAT Math Practice Question #291

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 \( 14 \). When \( P(x) \) is divided by \( x + 1 \), the remainder is \( -4 \). If \( P(x) \) is exactly divisible by \( x - 1 \), what is the value of the constant \( c \)?
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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

Let's break this down step-by-step. The SAT is testing your mastery of the Polynomial Remainder Theorem, which states that the remainder of a polynomial \( P(x) \) divided by \( (x - k) \) is simply \( P(k) \). First, translate the given in...

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

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