Answered: Find the quotient and the remainder by…

Find the quotient and the remainder by synthetic division of the polynomial P(x) for the given polynomial x - c. Write your answer in the form P(x) = Q(x) D(x) + R. Show your solution.

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter6: Fractions

Section6.1: Simplifying Fractions

Problem 31WE

See similar textbooks

Related questions

Q: For the given polynomial P (x) and the given c, use the remainder theorem to find P (c). P (x) =…

Q: Given that (x+1) is a FACTOR of the polynomial, find all the ROOTS of the polynomial

Q: Consider the polynomial equation of P(r) = 0 where P(x) = #* – a* – ² – a – - 2. - T (a) What are…

A: The given polynomial is Px=x4-x3-x2-x-2.

Q: Given f(x) = (x−2)^3(−x+ 1)^7(2x+ 6)^2(x+ 4) determine the following: (a) What is the leading (or…

A: The given function is- f(x) = (x−2)3(−x+ 1)7(2x+ 6)2(x+ 4) (a) The leading term of the polynomial is…

Q: For the given polynomial P(x) and c = , use the remainder theorem to find P(c). 2' P(x) = x° +x* +x°…

A: Here , given polynomial is Px=x5+x4+x3+5We have to calculate PCat C=12 by using remainder…

Q: Use synthetic division to decide whether the given number k is a zero of the polynomial function. If…

A: For synthetic division we find the coefficients of x^2+3x+2.That is 1,3,2

Q: 9. For the polynomial f(x) = x(3x + 1)(x – 2)², determine the leading coefficient, leading term,…

A: Given: fx=x3x+1x-22 Now solve the parenthesis we get, ⇒fx=3x4-11x3+8x2+4x ...(1)…

Q: A polynomial function P is given. P(x) = −x3 + 5x2 + 14x (a) Express the function P in factored…

Q: Find the rational zeros of the function h(x) = x3 − 19x + 30.

A: Given: h(x)=x3−19x+30

Q: Consider the polynomial P (x)=kx' - 5x +3x + 2. Find the value of k such that the remainder is 4…

A: The polynomial is given by Px = kx3-5x2+3x+2 The remainder obtained after dividing the polynomial Px…

Q: H.W:- find the root of the polynomial below:- 5 x³+ 4x1-3x³+2x²+x+1=0

A: The roots of a polynomial are those values of the variable that cause the polynomial to evaluate to…

Q: For the polynomial function A(x) = 2æ³ + 5a2 –28x–15 we know (x + 5) is a factor. Rewrite A(x) as a…

Q: Use the given information about the polynomial graph to write the equation. Degree 5 zeros at x =…

A: Given:- Use the given information about the polynomial graph to write the equation. Degree 5 zeros…

Q: Consider the polynomial P (x)=kx' + 3x + 4x + 2. 3. 2. %3D Find the value of k such that the…

A: The solution of the problem is given in the next step.

Q: Approximate the roots of the polynomial f(x) = X3 - 7X + 6 using Bolzano method.

Q: Find the critical points, A and B, of the following polynomial (with A<B). f(x)=2x3-294x+6 A= ?…

A: The given polynomial is fx=2x3-294x+6.

Q: (a) The degree of the polynomial is and the leading coefficient is

A: a. degree of the polynomial is 3 (since height power of x is 3) leading coefficient is 3 (because…

Q: Given that (x + 2) is a factor of the polynomial 2a – 5x2 + ax + a, the - value of the constant a is

A: If (x+2) is factor of the polynomial 2x3-5x2+ax+a then remainder will be zero when we divide (x+2)…

Q: For the polynomial P(x) = (x3 − 3x2 − 4x + 12)(2x3 + 5x2 − x − 6) Write the polynomial in factored…

A: Given data: The expression for the polynomial is P(x)=(x3-3x2-4x+12)(2x3+5x2-x-6). 1) The given…

Q: Graph the polynomial f(x) =x^3+3x^2−4 noting the x- and y-intercepts, multiplicity, and end…

A: Given, fx=x3+3x2-4 The graph of the given polynomial is,

Q: Find the value of p from the polynomial x2 +3x+p if one of the zeroes of the polynomial is 2

Q: 10 h(x) = x³ + 5x² - 4x- 20 %D

Q: Find a polynomial of degree four that has zeros -3, 0, 1, and 5, and the coefficient of x3 is -6.

A: We need to find a polynomial of degree four that has zeros -3, 0, 1, and 5, and the coefficient of…

Q: Determine the degree of the polynomial P(x) and arrange the terms in decreasing order. 4x3 - 3 +…

A: Polynomial and its Degree.

Q: Find the p(3) if the polynomial function is defined by p(x)=2x3-x2+3x-2. Find p(x+1) if the…

A: Given: px=2x3-x2+3x-2 px=3x2+7x+24

Q: Given the polynomial: f (x) = 2x° + mx* – 40x° + nx² + 218x – 168 And that two of the roots are x= 1…

Q: Determine the degree of the polynomial P(x) and arrange the terms in decreasing order. 6x + 5 - 5x4…

Q: For the given polynomial P(x) and the given c, use the remainder theorem to find P(c). P(x) = x°…

A: Given: The polynomial Px=x3+5x2-2x+4 and c=3 To find: P3 using remainder theorem.

Q: Determine the degree of the polynomial P(x) and arrange the terms in decreasing order. 2x2 – 7 + x…

Q: We want to find the zeros of this polynomial: p(x) = 2x + 3x – 18x- 27 %3D Plot all the zeros…

A: 2x^3+3x^2-18x-27 We apply synthetic division we will get (2x+3)(x+3)(x-3)=0 x=-3/2, 3 ,-3

Q: The polynomial p(x) has the rest (x+2) when dividing it by (x^2+2x-3) and the rest 1 when dividing…

A: We have given that p(x) leaves the remainder (x+2) when divided by x2+2x-3 and p(x) leaves the…

Q: Find a polynomial f (x) of degree 4 that has the following zeros. 4, -5, 0, -2 Leave your answer in…

A: Write in factor form

Q: Find a polynomial equation with real coefficients that has t 8, 9-i The polynomial equation is

Q: Consider the polynomial equation of P(x) = 0 where P(x) = x* – x3 – 2² – r – 2. (h) Find all zeros…

A: We will find the zeros of polynomial as shown below

Q: Find the zeroes of the polynomial f(x)=x3-12x2+39x-28 ,if it is given that the zeros are in AP

Q: Given p(x) = 29x13 + 9x11 - 8x9 + 25x2 + 3x - 97 is a polynomial of degree n what is an-1

Q: Find the degree of the polynomial function. h(x) = -6x + 9

A: Solution: The given expression is h(x)=-6x+9

Q: 2) Determine the end behavior, all the intercepts, and use that information to sketch the graph of…

Q: For a polynomial equation P(x) = 0, if P(x) is not factorable, then P(x) = 0 has no real roots.…

A: For a polynomial equation P(x) = 0, if P(x) is not factorable, then P(x) = 0 has no real roots.

Q: Consider the division f(x) ÷ (x – k) where f(x) = (x + 8)²(x – 8)(x + 5)³. (a) What is the remainder…

Q: For the given polynomial P(x) and the given c, use the remainder theorem to find P(c). P…

Q: find the value of the parameter m so that the remainder of the division of the polynomial P (x) =…

A: Solution: We have to find the value of m so that the remainder is -66 when Px=3x3-mx2+5x-6 is…

Q: Use the Factor Theorem to show that the statement in the exercise is true.

Q: Consider the polynomial g(x) (x - 1)(2x + 1)(3z –1)(5x + 1). A. What are the roots of g? B. Suppose…

Q: Given that 5x - 2is a factor of polynomial functions f(x) kx- bx + 2k, %3D determine the ratio k: b…

A: Given that 5x-2 is a factor of polynomial functions f(x)=kx2-bx+2k.

Q: The polynomial function q(x) = 3x + 11x2 - 14x- 40 has a known factor of (3x+5). Rewrite g(x) as the…

A: Given, polynomial function qx=3x3+11x2−14x−40 and known factor 3x+5 To write: qx as the product of…

Q: Consider the polynomial function P(x) = x* – 3x³ + ax² – 6x + 14, where a is an unknown real number.…

A: Given, Px = x4-3x3+ax2-6x+14 a is an unknown real number . x-2 is a factor of the polynomial. We…

Q: Find the polynomial of the specified degree whose graph is shown. Degree 4 P(x) = y 6F 5 4 2 1 + x…

A: It has zeros at x=-1 and x=2. So, it includes x+1 and x-2.

Q: Jae is constructing an open box from a plece of cardboard that is 9 in. wide and 12 in. long. He…

A: Given Data: The width of the cardboard is: w=9 in. The length of the cardboard is: l=12 in. The…

Question

Find the quotient and the remainder by synthetic division of the polynomial P(x) for the given polynomial x - c. Write your answer in the form P(x) = Q(x) D(x) + R. Show your solution.