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Test Citadel features an authentic Bluebook-calibrated countdown timer with visibility toggle, question navigation grid, choice eliminator cross-out tool, embedded Desmos graphing calculator, and official College Board formula sheets.

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Yes. Every visitor can complete 4 free diagnostic problems (2 Math with Desmos and 2 Reading & Writing) with full Socratic explanations before upgrading to Citadel Pro.

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SAT Math Difficulty: Hard (800) • Calibrated to 2026 Testing Standard

Digital SAT Math Practice Question #657

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

The polynomial $ p(x) = ax^3 + bx^2 + cx + d $ has distinct zeros at $ x = -2 $, $ x = 1 $, and $ x = 3 $. The polynomial $ q(x) $ is defined as $ q(x) = p(x) - 4 $. If $ q(x) $ is divisible by $ (x - 2) $, what is the $ y $-intercept of the graph of $ y = p(x) $ in the $ xy $-plane?

Select Your Answer:

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 is a masterpiece of a polynomial question that combines factored form, the Factor Theorem, and the Remainder Theorem. Let's attack it step-by-step. Step 1: Write $ p(x) $ in factored form. Since $ p(x) $ is a cubic polynomial with ...

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

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