SAT Math Practice Question #596 (Hard (800)) | Test Citadel
TC
Test Citadel
SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #596

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

Let \( P(x) = x^4 + ax^3 + bx^2 + cx + d \), where \( a, b, c, \) and \( d \) are constants. When \( P(x) \) is divided by \( x^2 - 1 \), the remainder is \( 3x + 2 \). When \( P(x) \) is divided by \( x^2 - 4 \), the remainder is \( 5x - 1 \). What is the value of \( d \)?
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)

Elimination Shortcut: Check the extremes or test answer choices starting with C to binary search the correct magnitude.

Masterclass Solution & Distractor Trap Analysis

This problem tests your deep conceptual understanding of the Polynomial Remainder Theorem and system of equations. Step 1: Understand the Remainder Theorem application. The division algorithm states that \( P(x) = Q(x) \cdot D(x) + R(x) \)....

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

🔒 Citadel Pro Scholar Vault

Unlock Full Solution & 2,600+ Official Drills

Access detailed Socratic steps, trap breakdowns, authentic timed module simulations, and Desmos speed hacks for just $9.99/mo.

Socratic Assistant

Targeted hints without disclosing final solutions.

I am your Socratic tutor. Click one of the quick guidance buttons above or ask a specific question below about a formula or method.