SAT Math Practice Question #438 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #438

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

The equation \( \frac{6x^3 - 13x^2 + 21x - k}{3x - 2} = 2x^2 - 3x + 5 + \frac{7}{3x - 2} \) is true for all values of \( x eq \frac{2}{3} \), where \( k \) is a constant. What is the value of \( k \)?
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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)

Desmos Tactical Shortcut: Plot the left-hand side and right-hand side as separate equations (e.g. \( y_1 = f(x) \) and \( y_2 = g(x) \)). Click the intersection points directly to read exact coordinates.

Masterclass Solution & Distractor Trap Analysis

This problem involves 'Polynomial Division' and 'Rational Equations.' When you see an expression like this, the absolute fastest way to conquer it is to clear the denominator. Step 1: Multiply the entire equation by the denominator \( (3x -...

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

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