Answered: When the expression x^4 + ax^3 + 5x^2 +…

When the expression x^4 + ax^3 + 5x^2 + bx + 6 is divided by (x – 2), the remainder is 16. When it is divided by (x + 1) the remainder is 10. Determine the value of the constant a.

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

Chapter4: Polynomials

Section4.4: Powers Of Monimials

Problem 12OE

See similar textbooks

Related questions

Q: The plane contains the point P(-1,2,-4) and the line l:r=(2i−5 j−3k)+t(−4i+2j+k) Show that the…

Q: A vector function is given as A = x(x-4) ey/6 cos(zπ/2) What is the result of (VA) dv over the…

A: As per the question we are given the following vector field : A = (x - 4)ey/6 cos(zπ/2) And the…

Q: If the determinant of the first matrix below is as given, find the determinant of the other matrix.…

Q: Given P = “Grisha was able to finish the tactical training course as top of the class.”, given Q =…

Q: Find the production matrix for the following input-output and demand matrices using the open model.…

Q: For the data table below, answer the following questions. Data table: X 2 4 7 Y 2 8 12 Questions:…

A: Given: x 2 4 7 y 2 8 12 To Do: (a) Write a system of equations to determine the coefficients…

Q: Problem #1: Let T: P3 → R³ be the linear transformation defined as [P(-1) p(1) P(2) Which of the…

Q: For the Euler Axis and Principal Angle, demonstrate that: v₁DCM²¹: = cos v₁ + sin Ov₂ v₂DCMe' sin…

A: To prove :v¯1eDCMe'=cosθ v1¯+sinθ v2¯v¯2eDCMe'=-sinθ v1¯+cosθ v2¯

Q: Find all numbers "a" such that a³ = -1.

Q: Solve the following linear congruences (you may if you wish, find some solutions by inspection): (a)…

Q: For the Euler Axis and Principal Angle, demonstrate that: v₁DCM²¹ = cos 0v₁ + sin №v₂ v²DCM²' = —…

A: We want to show that :v¯1eDCMe'=cosθ v1¯+sinθ v2¯v¯2eDCMe'=-sinθ v1¯+cosθ v2¯

Q: Find the optimal simplex tableau at the end of Phase I with row0 at the bottom for the following LP:…

A: Given, MAX Z = 280x1 + 40x2 + 500x3 + 510x4subject to30x1 + 5x2 + 45x3 + 60x4 <= 5000x1 - 5x2 +…

Q: 5. Consider the system of equations 2x + 4y = -2 -x + 3y = 6 (a) Write down the tabular form of this…

Q: d villual Sept 2022 c. Use the Remainder Theorem to determine the remainder when 2x³-3x² - 4x+5 is…

Q: Q(3): Show that: (a) Vx Vo(r) = 0, and (b) V-VX E(F) = 0.

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: it looks like part c and part d were cut off (just says U( and we dont see what L(f)< in part d…

A: As per the instructions we will do the subparts (b), (c) and (d). As per the question we are given…

Q: Find the real root correct to three decimal places for the following equations: (i) x³ x 4 = 0 (ii)…

A: Given: a) x3-x-4=0 b) x3-x2-1=0 To Find: The real root of the above equation.

Q: Let P(A) = P(B) = and P(ANB) = . Find the following: (a) P(A¹). (b) P(A' B'). (c) P(BNA'). (d)…

Q: Find the absolute extrema if they exist, as well as all values of x where they occur, for the…

Q: Find all the values of x such that the given series would converge. (-1)" xn n+ 3 Answer: [-1,1] n=1

A: I have explained everything with in the solution. Please go through that.

Q: Question 11 What type of shaded region Venn diagram is shown below? A B 1 2 3 4 OA UB O AUB OA UB OA

Q: 1. Find the cube roots of −1+√3i then represent each root in the argand plane

Q: 1-47 Evaluate the integral. 1. f sin'x cos³x dx 3.sin³x cos'x dx 5. f cos³x sin'x dx w/2 7. ² cos³0…

A: Since you have posted a question with multiple subparts, so we will solve only the first three…

Q: Find f'(x). 4 f(x) = 2x* Inx f'(x) =

A: Given, f(x)=2x4lnx To find: f'(x)

Q: Let X-U[0, 2]. Compute the pdf of Y if Y = g(X), where the function g is plotted as lg(x) A 1 +-1N X

Q: 2. Find the polynomial interpolation of y = cos a close to the point x = 0 by (a) Evaluating the…

A: Introduction: Polynomial interpolation is a method for approximating a function f(x) with a…

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT 3) Stan(x) dx

A: The answer provided below has been developed in a clear step by step manner.

Q: d. Prove that the ring of polynomial R[X] is also an integral domain. e. In Z₁[X], show that (2x+1)²…

Q: Determine whether the matrix is a regular stochastic matrix. A= 0.2 0 0.8 1 Is the matrix A a…

Q: 25.1. Expand each of the following functions f(z) in a Laurent series on the indicated domain: (a).…

Q: For the Euler Axis and Principal Angle, demonstrate that: v₁DCM²¹: = cos v₁ + sin Ov₂ v₂DCM²' = −…

A: Here,We want to show that :v¯1eDCMe'=cosθ v1¯+sinθ v2¯v¯2eDCMe'=-sinθ v1¯+cosθ v2¯

Q: et f: RR such that f(x): = -x if x is rational and f(x) = 2x+3 if x is irrational. ove that f is…

A: Continuity of the function

Q: THEOREM OF THE GENERAL SOLUTION. Let x1(t),…,xn(t) be n linearly independent solutions of the system…

A: The given information is that we have a system of linear differential equations of the form X' =…

Q: Let f, g be differentiable functions on [a, b] and their derivatives f', g' be integrable on [a, b].…

Q: 2. Let f be integrable on [a, b] and continuous at c E (a, b). Show that rc+h for f(x)da = f(c). c-h…

Q: 16. Evaluate and simplify (4 +9i)² a. 97 + 72i b. -65+72i 16 + 721 +81i² C. d. -65

Q: let AABC be a triangle S². Let the dual point C'ES² of C be defined by the following three…

A: Given: △ABC is a triangle S2 (the two-dimensional sphere). The dual point C'∈S2 of C is described by…

Q: · cos(2a) cosh (a)=-1¶ ¶ Solve it to obtain 1 1.875 a and = 4.693 a

Q: This question concerns the vector field F = -ry²i-r²yj + z(x² + y²) k. (a) Calculate the divergence…

Q: 2. Consider the following matrices: 1 1 0 10 1 € M3x3(Z₂), 0 1 1, (3) 2 1 1 2 € M3x2(Z3), 112 2001…

A: The given matrices are, A=110101011, A=211221, and A=112120011121. (a) To Find: Reduced row echelon…

Q: 3. (a) It follows from Sylow's (First) Theorem that if G is a finite p-group (for some prime p),…

A: Introduction: Isomorphism is a concept in mathematics that describes a type of relationship between…

Q: 12. Laplace transform is used to convert function in terms of distance into a function in terms of…

A: 12. Laplace transform is used to convert function in terms of distance into a function in…

Q: 3. Let R (a) go f is also a ring homomorphism. (b) If f, g are isomorphisms, then so is go f. (c) If…

Q: Set A = |{ { A, B, }, {5,1 }, {1,3,5 }, { 3}, { 2,3} }|. How many elements are in this set?

A: We have to find number of elements in set A

Q: In excercise 6 Find the inverse of the given matriu (pfft exists) using Theorem 3.8 6:11/√2. -1/2…

Q: Solve y" = 3; y(0) = 0, y'(0) = 0 using Laplace transforms.

A: The given initial value problem y''=3, y0=0, y'0=0. We have to solve this problem using the Laplace…

Q: Find the first four nonzero terms of the Taylor series about 0 for the function f(x) = √1 + x…

Q: The operation Management Computer Lab at the PUPR has two student software statistical package…

A: To develop the arrival equation, we need to use the triangular distribution to determine the…

Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

Q: A remote village receives radio broadcasts from two radio stations, a news station and a music…

Question

When the expression x^4 + ax^3 + 5x^2 + bx + 6 is divided by (x – 2), the remainder is 16. When it is divided by (x + 1) the remainder is 10. Determine the value of the constant a.

Expert Solution