SAT Math Practice Question #922 (Hard (800)) | Test Citadel
TC
Test Citadel
SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #922

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

The polynomial function \( P \) is defined by: \[ P(x) = 4x^3 + mx^2 - 2x + 7 \] where the variable coefficient is a constant. When \( P(x) \) is divided by \( (x - 1) \), the remainder is 12. What is the value of the unknown coefficient?
Select Your Answer:
Socratic AI Engine Step-by-Step Derivation
0ms Precomputed
Tactical Insight (Hint 1)

Recall the Remainder Theorem: if a polynomial \( P(x) \) is divided by \( (x - c) \), the remainder is simply \( P(c) \).

Elimination Framework (Hint 2)

Desmos Shortcut: Enter the polynomial with a slider for the variable. In the next line, evaluate \( P(1) \) and adjust the slider until it equals 12.

Masterclass Solution & Distractor Trap Analysis

By the Polynomial Remainder Theorem, dividing \( P(x) \) by \( (x - c) \) results in a remainder equal to \( P(c) \). Here, \( c = 1 \) and \( P(1) = 12 \). Substitute \( x = 1 \) into \( P(x) \) and equate to 12 to solve for the missing co...

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.