SAT Math Practice Question #636 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #636

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

In the \( xy \)-plane, the graph of \( y = x^4 - 2x^3 + kx^2 + mx - 8 \) intersects the \( x \)-axis at \( (2, 0) \). If the remainder when the polynomial is divided by \( (x + 1) \) is \( -15 \), what is the \( y \)-coordinate of the \( y \)-intercept of the graph of \( y = kx + m \)?
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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)

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 question brilliantly combines the Remainder Theorem, roots of polynomials, and linear graphs. Step 1: Use the given root. We are told the graph intersects the \( x \)-axis at \( (2, 0) \). This means that when \( x = 2 \), \( y = 0 \)....

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

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