SAT Math Practice Question #668 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #668

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

The polynomial \( p(x) = x^3 + kx^2 + mx + 24 \) is divisible by \( (x - 2) \). When \( p(x) \) is divided by \( (x - 1) \), the remainder is \( 30 \). What is the value of \( k - m \)?
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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 crack this advanced polynomial question using a powerful tool: the Polynomial Remainder Theorem! The Remainder Theorem states that when a polynomial \( p(x) \) is divided by \( (x - c) \), the remainder is exactly equal to \( p(c) \)....

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

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