(a) Divide x5and remainder r(x). Verify that the quotient times x – x² + 1 plus theremainder is the original polynomial.x4 + 3x3 + 2x²x + 1 by x3 – x² + 1, finding the quotient q(x)(b) What is the degree of the polynomial 2+ 4x + 6x? + 8x³ + 10x4 + 12x°? Write itin summation notation.

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Divide x – x4 + 3x³ + 2x2 – x + 1 by x³ – x² + 1, finding the quotient q(x) and remainder r(x). Verify that the quotient times x3 – x2 + 1 plus the remainder is the original polynomial. What is the degree of the polynomial 2+ 4x + 6x² + 8x³ + 10x4 + 12x? Write it in summation notation.

Divide x – x4 + 3x³ + 2x2 – x + 1 by x³ – x² + 1, finding the quotient q(x) and remainder r(x). Verify that the quotient times x3 – x2 + 1 plus the remainder is the original polynomial. What is the degree of the polynomial 2+ 4x + 6x² + 8x³ + 10x4 + 12x? Write it in summation notation.

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 17E: Use the Remainder Theorem to find the remainder that occurs when P(x)=3x4+5x34x22x+1 is divided by...

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Question

(a) Divide x5
and remainder r(x). Verify that the quotient times x – x² + 1 plus the
remainder is the original polynomial.
x4 + 3x3 + 2x²
x + 1 by x3 – x² + 1, finding the quotient q(x)
(b) What is the degree of the polynomial 2+ 4x + 6x? + 8x³ + 10x4 + 12x°? Write it
in summation notation.

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