wo polynomials P and D are given. Use either synthetic or long division to divide P(x)by D(x),and express the quotient P(x)/D(x) in the form P(x)/D(x)= Q (x)+R(x)/D(x). P(x) = 2x3 + 4x2 − 2x − 1, D(x) = x + 3 P(x)/D(x)=

wo polynomials P and D are given. Use either synthetic or long division to divide P(x)by D(x),and express the quotient P(x)/D(x) in the form P(x)/D(x)= Q (x)+R(x)/D(x). P(x) = 2x3 + 4x2 − 2x − 1, D(x) = x + 3 P(x)/D(x)=

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter3: Polynomial And Rational Functions

Section3.3: Dividing Polynomials

Problem 44E: Remainder Theorem Use synthetic division and the Remainder Theorem to evaluate P(c) ....

See similar textbooks

Related questions

Q: Use synthetic division to factor f(x) = - 10z³ + 15x² + 40x + 15 given f( – 1) = 0 A) Fill in the…

A: Synthetic division

Q: find the zeros and their multiplicities. consider using descartes' rule of sign and the upper and…

Q: An advertising company uses the function R(x) = - 2x + 13x2 + 4x + 45 to model expected annual…

A: According to the question, An advertisement company uses the function R(x) = -2x3 + 13x2 + 4x + 15…

Q: P(x) Two polynomials P and D are given. Use either synthetic or long division to divide P(x) by…

A: Given: The two polynomials are, Px=2x2-5x-2Dx=x-2 To find: Divide the polynomials and write it in…

Q: f(x) = 2x3 - 3x2 - 11x + 6 a. List all possible rational zeros.b. Use synthetic division to test the…

Q: 1 Synthetic Division of Polynomials Find the quotient and remainder using synthetic division. 2r –…

Q: Use synthetic division to find the value of ( x + 1) for P (x ) = x6 – x4 - x2 +…

A: Since you have posted a multiple questions , we will solve the first for you. To get the remaining…

Q: 1. Compare and contrast the usefulness of the remainder theorem and long division. b. Do you…

A: Remainder theorem: If any polynomial is divided by a linear polynomial (x-a), then the remainder is…

Q: wo polynomials P and D are given. Use either synthetic or long division to divide P(x) by D(x), and…

Q: f(x) = x3 + x2 - 4x - 4 a. List all possible rational zeros.b. Use synthetic division to test the…

Q: f(x) = 3x3 - 9x2 - 12x + 6 a) Find the remainder when f(x) is divided by (x-4). b) Use the factor…

Q: R(x). = Q(x) + D(x) D(x) Two polynomials P and D are given. Use either synthetic or long division to…

Q: A polynomial f(x) and a factor of f(x) are given. Factor the polynomial completely using synthetic…

Q: R(x) D(x) Two polynomials P and D are given. Use either synthetic or long division to divide P(x) by…

A: Given: The polynomial Px=6x2-3x-11 and Dx=3x-1, TO determine: PxDx in the form of PxDx=Qx+RxDx.

Q: (4x^2 − x − 23) ÷ (x-1) use polynomial long division to perform the indicated division. Write the…

A: Consider the division (4x2-x-23)/ (x-1).Here, the dividend is 4x2-x-23 and the divisor is x-1.

Q: Use synthetic division to find the value P ( 4) for P (x ) = x3 -2x2 - 5x - 7…

A: Using synthetic division to find indicated values.

Q: 1. In Unit 1 you have learnt about the remainder theorem and long division. Compare and contrast the…

A: Hello. Since your question has multiple parts, we will solve first three parts for you. If you want…

Q: Subtask I of 2: Perform division of polynomials using long divir Activity 1: FIND and SHOW ME THE…

A: Given:Long division methodPx=x-aQx+rx

Q: 1 Synthetic Division of Polynomials Find the quotient and remainder using synthetic division. x +…

A: given that x3+2x2+2x+1x+2 we need to find the quotient and remainder from the synthetic division of…

Q: Analyze the polynomial function f(x)=x^2(x+9) using parts (a ) through (e). The lesser zero of the…

A: Here we have to draw the polynomial f(x) = x2 ( x + 9) and analysis the polynomial function.…

Q: onstruct a polynomial function with the stated properties. Reduce all fractions to lowest terms.…

Q: 15-24 - Long Division of Polynomials remainder using long division. Find the quotient and x³ + 2x?…

A: Given, x6+x4+x2+1x2+1

Q: Given the polynomial function P(x)= 3x³ – 5x² –-4x+4. (a) List all possible rational zeros of P. (b)…

Q: p(x)=x^3-2x^2-4x+5 Select all intervals for which the above polynomial is increasing & decreasing.

Q: 2 Is a simplified method for dividing a polynomial by another polynomial with degree 1. A. Synthetic…

A: (2) Long method division (3) Remainder theorem

Q: Use synthetic division to find the value of ( x - 6 ) for P (x ) = 1 - 7x - 4x2…

Q: f(x) = 3x3 - 9x2 - 18x + 18 a) Find the remainder when f(x) is divided by (x-4). b) Use the…

Q: Two polynomials P and D are given. Use either synthetic or long division to divide P(x) by Dx), and…

Q: Use synthetic division and the Remainder Theorem to evaluate P(c). P(x) = 4x3 + 13x² – 5x + 3, C = 5…

Q: Jse synthetic division to show that x is a solution of the third-degree polynomial equation, and use…

Q: Using long division, you can calculate that 2x3 – 4x2 + 7x – 6 R(x) Q(x) + 2x2 + 5 - f(x) = 2x2 + 5…

Q: R(x) D(x) Р(x) D(x) Two polynomials P and D are given. Use either synthetic or long division to…

A: Given,

Q: 2. If the result of a polynomial division is 2x3 - 4x2 - 5x + 23/x + 2 .make at least three…

A: “Since you have asked multiple question, we will solve the one question for you. If you want any…

Q: P(x) = Q(x) + D(x) R(x) D(x) Two polynomials P and D are given. Use either synthetic or long…

A: we divide p(x) by d(x).and get the solution in 2nd step.

Q: Given the polynomial function P(x)=3x°-2x-7x-2. (a) List all possible rational zeros of P. (b)…

Q: Use synthetic division if possible. You can use synthetic division if you are dividing by x - c. 6x…

Q: polynomial, resulting in the given quotie remainder. Determine the dividend. a) divisor: x – 9,…

Q: 1 Remainder Theorem Use synthetic division and the Remainder Theorem to evaluate P(c). 39. P(x) =…

Q: wo polynomials P and D are given. Use either synthetic or long division to divide P(x) by D(x), and…

Q: Applying Eisenstein's criterion to verify if a polynomial is irreducible or not. For example:…

A: Yes it is correct For example: x^3+4x^2+3 We choose p=3. We can't apply Eisenstein's criterion…

Q: Given the polynomial function P(x)=3x³-5x2-4x+4. (a) List all possible rational zeros of P. (b)…

Q: 3. (8 points) Let h(x) = x³+3x2 –13x+15. Express h(x) in the form h(x) = (x-3)q(x)+r. Use the…

Q: Given the polynomial function P(x)= 3x³+8x²+3x-2. (a) List all possible rational zeros of P. (b)…

A: To find the y intercept

Q: f(x) = 3x3 - 7x2 - 12x + 4 a) Find the remainder when f(x) is divided by (x-4). b) Use the factor…

Q: 15. Given the polynomial x + 3x - 10x 24 , use synthetic division a). write all the factors of the…

Q: Polynomial division (where D(x)#0) can be used to change any polynomial in standard form into the…

Q: wo polynomials P and D are given. Use either synthetic or long division to o x)/D(x) in the form…

Q: Given the polynomial function P(x)=3x³+8x²+ 3x-2. (a) List all possible rational zeros of P. (b)…

Q: wo polynomials P and D are given. Use either synthetic or long division to divide P(x) by D(x),…

Concept explainers

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.

Question

100%

wo polynomials P and D are given. Use either synthetic or long division to divide P(x)by D(x),and express the quotient P(x)/D(x) in the form P(x)/D(x)= Q (x)+R(x)/D(x).

P(x) = 2x³ + 4x² − 2x − 1, D(x) = x + 3

P(x)/D(x)=

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2 Solution

VIEW

Step 3 Final solution

VIEW

Step by step

Solved in 3 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Polynomial$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

Remainder Theorem Use synthetic division and the Remainder Theorem to evaluate P(c) . P(x)=2x321x2+9x200, c=11
Number of Intercepts and Local Extrema How many x-intercepts and how many local extrema does the polynomial P(x)=x34x have? How many x-intercepts and how many local extremadoes the polynomial Q(x)=x3+4x have? If a > 0. bow many x-intercepts and how many local extrema does each Of the polynomials P(x)=x3ax and Q(x)=x3+ax have? Explain your answer.
The polynomial P(x)=5x2(x4)3(x+7) has degree ___________. It has zeros 0, 4, and ______________. The zero has multiplicity _________
DISCOVER: Nested Form of a Polynomial Expand Q to prove that the polynomials P and Q are the same. P(x)=3x45x3+x23x+5 Q(x)=(((3x5)x+1)x3)x+5 Try to evaluate P(2) and Q(2) in your head, using the forms given. Which is easier? Now write the polynomial R(x)=x52x4+3x32x2+3x+4 in nested form, like the polynomial Q. Use the nested form to find R(3) in your head. Do you see how calculating with the nested form follows the same arithmetic steps as calculating the value of a polynomial using synthetic division?
Using Descartes’ Rule of Signs. we can tell that the polynomial P(x)=x53x4+x2+8x8 has _______________, ____________________positive real zeros and _____________negative real zeros.