SAT Math Practice Question #287 (Hard (755)) | Test Citadel
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SAT Math Difficulty: Hard (755)

Digital SAT Math Practice Question #287

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The rational expression \( \frac{3x^3 + 4x^2 + x - 15}{x + 2} \) is equivalent to the expression \( A x^2 + B x + C + \frac{D}{x + 2} \) for all \( x eq -2 \), where \( A \), \( B \), \( C \), and \( D \) are constants. 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)

Substitution Tactic: Test simple numbers for variables (like \( x = 2 \) or \( x = 3 \)), calculate the numeric target, and evaluate the choices to see which matches.

Masterclass Solution & Distractor Trap Analysis

We are given a cubic polynomial divided by a linear binomial, and the result is in the form of a quotient (\( Ax^2 + Bx + C \)) plus a remainder over the divisor (\( \frac{D}{x + 2} \)). We need to find the sum of all the coefficients, \( A...

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

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