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Let f(x) be a polynomial with real coefficients. The polynomial f(x) leaves the remainder 2x +1 when it is divided by 3x² + 1 and leaves the remainder 6x – 1 when it is divided by x² + 3. Find the remainder when f(x) is divided by 3x + 10x² + 3.

Let f(x) be a polynomial with real coefficients. The polynomial f(x) leaves the remainder 2x +1 when it is divided by 3x² + 1 and leaves the remainder 6x – 1 when it is divided by x² + 3. Find the remainder when f(x) is divided by 3x + 10x² + 3.

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter4: Polynomial And Rational Functions
Section4.3: The Remainder And Factor Theorems; Synthetic Division
Problem 4E
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Let f(x) be a polynomial with real coefficients. The polynomial f(x) leaves the remainder 2x +1 when it is divided by 3x? + 1 and leaves the remainder 6x – 1 when it is divided by x² + 3. Find the remainder when f(x) is divided by 3x + 10x² + 3.
Transcribed Image Text:Let f(x) be a polynomial with real coefficients. The polynomial f(x) leaves the remainder 2x +1 when it is divided by 3x? + 1 and leaves the remainder 6x – 1 when it is divided by x² + 3. Find the remainder when f(x) is divided by 3x + 10x² + 3.
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