SAT Math Practice Question #730 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #730

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 roots at \( x = -2 \), \( x = 3 \), and \( x = 5 \). If \( p(x) \) is divided by \( x - 4 \), the remainder is \( -12 \). What is the \( y \)-intercept of the graph of \( y = p(x) \) in the \( xy \)-plane?
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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 beautiful problem tests your knowledge of the Factor Theorem, the Remainder Theorem, and polynomial intercepts. Let's conquer it step-by-step. Step 1: Construct the factored form of the polynomial. We are told the polynomial has roots ...

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

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