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Home » \[ y = rac2x + 3x - 1 \] - Red Crowns

\[ y = rac2x + 3x - 1 \] - Red Crowns

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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\( \log_2(x(x - 2)) = 3 \) → \( x(x - 2) = 2^3 = 8 \).
\( x^2 - 2x - 8 = 0 \) → \( (x - 4)(x + 2) = 0 \).
\( x = 4 \) (since \( x > 2 \) for log to be defined).
The graph of \( y = a \cdot 2^x \) passes through the points $ (0, 3)...
At \( x = 0 \): \( y = a \cdot 2^0 = a = 3 \).
Check with \( x = 2 \): \( y = 3 \cdot 2^2 = 12 \), which matches.
So \( a = 3 \).
What is the remainder when \( x^4 - 3x^2 + 2x + 5 \) is divided by \(...
Use Remainder Theorem: evaluate at \( x = 1 \).
\( 1^4 - 3(1)^2 + 2(1) + 5 = 1 - 3 + 2 + 5 = 5 \).

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