5. Compare the number of multiplications and additions/subtractions neededby the "long division" of a polynomial p(x)=ªñx" +ªn_₁x²−¹ + ... + ªo byx -- c, where c is some constant, with the number of these operations in"synthetic division."

Answered: Image /qna-images/answer/6890bb59-b936-4f35-bf9c-d151c573d811.jpg

Answered: -1 . Compare the number of…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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#9 USE SYNTHETIC DIVISION TO FIND THE QUOTIENT AND REMAINDER
Open with 1.9.1 Dividing Polynomials (conunuer Using the previous example, complete the polynomial division questions below: 1. x'-5x-x-10 by x-2 2. 2y' +y'-27y-36 by y +3 4. 2x'-3x-8r-3 by 2x+1 3. y-28y-41 by y+4 ["note: y-28y-41-y +0y-28y-41]
2. Using either long division or x4-3x³+x²+6x–10 synthetic division: x-2
1) a. Apply Horner’s rule to evaluate the polynomial ?(?) = 3?5 − 2?4 + ?3 − 2? + 5 ?? ? = −2. b. Use the results of the above application of Horner’s rule to find the quotient and remainder of the division of ?(?) by ? + 2
Please answer these questions
1. refer to image use polynomial long division to evaluate the following quotients. Show your work.
#15
13. Use synthetic division to divide the following: A. {3, -6, -4} B. (3, 6, 4) C. {-3, -6, -4} ****** ...... D. {-3, 6, 4) ***** f(x) = x³ - 13x² +54x - 72 by x - 3
Consider the division f(x) ÷ (x – k) where f(x) = (x + 8)²(x – 8)(x + 5)3. (a) What is the remainder when k = -8?
1. A x) -3 x+2 and g( x) 20+ 5. Find fo g(5) v+)+5(メ5) 2. A x) - 2 x-4 and g( x) = 2x+ 8. Find go f x). 3. Given f(x)=x-1 and g(x)=x'+2x-8, find (gºf(x) Divide using Synthetic Division 1. 3x-9x +5x-18x²+5x+12 x-3
Consider f (x) = 2x* – x3 – 5x2 + 2x + 2. 1. List all possible zeros (candidates) for f(x). 2. Define f (x) in your calculator or desmos. Use the graph to narrow down your candidates. Use synthetic division to reduce f (x) to a quadratic expression. Factor the resulting quadratic expression to find the last two zeros. ZEROS: 3. Express f(x) as a product of linear factors. Don't forget to include the value of a!

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-1 . Compare the number of multiplications and additions/subtractions needed by the "long division” of a polynomial p(x)= ªñx” + ª₂-x²−¹ + ... + ao by x-c, where c is some constant, with the number of these operations in "synthetic division."