 5.4.5.1.408: Fill in each blank so that the resulting statement is true. The coe...
 5.4.5.1.409: Fill in each blank so that the resulting statement is true. The deg...
 5.4.5.1.410: Fill in each blank so that the resulting statement is true. The coe...
 5.4.5.1.411: Fill in each blank so that the resulting statement is true. The deg...
 5.4.5.1.412: Fill in each blank so that the resulting statement is true. True or...
 5.4.5.1.413: Fill in each blank so that the resulting statement is true. True or...
 5.4.5.1.414: In Exercises 16, evaluate each polynomial for x 2 and y 3. x2 2xy y2
 5.4.5.1.415: In Exercises 16, evaluate each polynomial for x 2 and y 3. x2 3xy y2
 5.4.5.1.416: In Exercises 16, evaluate each polynomial for x 2 and y 3. xy3 xy 1
 5.4.5.1.417: In Exercises 16, evaluate each polynomial for x 2 and y 3. x3y xy 2
 5.4.5.1.418: In Exercises 16, evaluate each polynomial for x 2 and y 3. 2x2y 5y 3
 5.4.5.1.419: In Exercises 16, evaluate each polynomial for x 2 and y 3. 3x2y 4y 5
 5.4.5.1.420: In Exercises 78, determine the coefficient of each term, the degree...
 5.4.5.1.421: In Exercises 78, determine the coefficient of each term, the degree...
 5.4.5.1.422: In Exercises 920, add or subtract as indicated. (5x2y 3xy) (2x2y xy)
 5.4.5.1.423: In Exercises 920, add or subtract as indicated. (2x2y xy) (4x2y 7xy)
 5.4.5.1.424: In Exercises 920, add or subtract as indicated. (4x2y 8xy 11) (2x2y...
 5.4.5.1.425: In Exercises 920, add or subtract as indicated. (7x2y 5xy 13) (3x2y...
 5.4.5.1.426: In Exercises 920, add or subtract as indicated. (7x4y2 5x2y2 3xy) (...
 5.4.5.1.427: In Exercises 920, add or subtract as indicated. (6x4y2 10x2y2 7xy) ...
 5.4.5.1.428: In Exercises 920, add or subtract as indicated. (x3 7xy 5y2) (6x3 x...
 5.4.5.1.429: In Exercises 920, add or subtract as indicated. (x4 7xy 5y3) (6x4 3...
 5.4.5.1.430: In Exercises 920, add or subtract as indicated. (3x4y2 5x3y 3y) (2x...
 5.4.5.1.431: In Exercises 920, add or subtract as indicated. (5x4y2 6x3y 7y) (3x...
 5.4.5.1.432: In Exercises 920, add or subtract as indicated. (x3 y3) (4x3 x2y xy...
 5.4.5.1.433: In Exercises 920, add or subtract as indicated. (x3 y3) (6x3 x2y xy...
 5.4.5.1.434: Add: 5x2y2 4xy2 6y2 8x2y2 5xy2 y2
 5.4.5.1.435: Add: 7a2b2 5ab2 6b2 10a2b2 6ab2 6b2
 5.4.5.1.436: Subtract: 3a2b4 5ab2 7ab (5a2b4 8ab2 ab)
 5.4.5.1.437: Subtract: 13x2y4 17xy2 xy (7x2y4 8xy2 xy)
 5.4.5.1.438: Subtract 11x 5y from the sum of 7x 13y and 26x 19y.
 5.4.5.1.439: Subtract 23x 5y from the sum of 6x 15y and x 19y.
 5.4.5.1.440: In Exercises 2776, find each product. (5x2y)(8xy)
 5.4.5.1.441: In Exercises 2776, find each product. (10x2y)(5xy)
 5.4.5.1.442: In Exercises 2776, find each product. (8x3y4)(3x2y5)
 5.4.5.1.443: In Exercises 2776, find each product. (7x4y5)(10x7y11)
 5.4.5.1.444: In Exercises 2776, find each product. 9xy(5x 2y)
 5.4.5.1.445: In Exercises 2776, find each product. 7xy(8x 3y)
 5.4.5.1.446: In Exercises 2776, find each product. 5xy2(10x2 3y)
 5.4.5.1.447: In Exercises 2776, find each product. 6x2y(5x2 9y)
 5.4.5.1.448: In Exercises 2776, find each product. 4ab2(7a2b3 2ab)
 5.4.5.1.449: In Exercises 2776, find each product. 2ab2(20a2b3 11ab)
 5.4.5.1.450: In Exercises 2776, find each product. b(a2 ab b2)
 5.4.5.1.451: In Exercises 2776, find each product. b(a3 ab b3)
 5.4.5.1.452: In Exercises 2776, find each product. (x 5y)(7x 3y)
 5.4.5.1.453: In Exercises 2776, find each product. (x 9y)(6x 7y)
 5.4.5.1.454: In Exercises 2776, find each product. (x 3y)(2x 7y)
 5.4.5.1.455: In Exercises 2776, find each product. (3x y)(2x 5y)
 5.4.5.1.456: In Exercises 2776, find each product. (3xy 1)(5xy 2)
 5.4.5.1.457: In Exercises 2776, find each product. (7xy 1)(2xy 3)
 5.4.5.1.458: In Exercises 2776, find each product. (2x 3y)2
 5.4.5.1.459: In Exercises 2776, find each product. (2x 5y)2
 5.4.5.1.460: In Exercises 2776, find each product. (xy 3)2
 5.4.5.1.461: In Exercises 2776, find each product. (xy 5)2
 5.4.5.1.462: In Exercises 2776, find each product. (x2 y2)2
 5.4.5.1.463: In Exercises 2776, find each product. (2x2 y2)2
 5.4.5.1.464: In Exercises 2776, find each product. (x2 2y2)2
 5.4.5.1.465: In Exercises 2776, find each product. (x2 y2)2
 5.4.5.1.466: In Exercises 2776, find each product. (3x y)(3x y)
 5.4.5.1.467: In Exercises 2776, find each product. (x 5y)(x 5y)
 5.4.5.1.468: In Exercises 2776, find each product. (ab 1)(ab 1)
 5.4.5.1.469: In Exercises 2776, find each product. (ab 2)(ab 2)
 5.4.5.1.470: In Exercises 2776, find each product. (x y2)(x y2)
 5.4.5.1.471: In Exercises 2776, find each product. (x2 y)(x2 y)
 5.4.5.1.472: In Exercises 2776, find each product. (3a2b a)(3a2b a)
 5.4.5.1.473: In Exercises 2776, find each product. (5a2b a)(5a2b a)
 5.4.5.1.474: In Exercises 2776, find each product. (3xy2 4y)(3xy2 4y)
 5.4.5.1.475: In Exercises 2776, find each product. (7xy2 10y)(7xy2 10y)
 5.4.5.1.476: In Exercises 2776, find each product. (a b)(a2 b2)
 5.4.5.1.477: In Exercises 2776, find each product. (a b)(a2 b2)
 5.4.5.1.478: In Exercises 2776, find each product. (x y)(x2 3xy y2)
 5.4.5.1.479: In Exercises 2776, find each product. (x y)(x2 5xy y2)
 5.4.5.1.480: In Exercises 2776, find each product. (x y)(x2 3xy y2)
 5.4.5.1.481: In Exercises 2776, find each product. (x y)(x2 4xy y2)
 5.4.5.1.482: In Exercises 2776, find each product. (xy ab)(xy ab)
 5.4.5.1.483: In Exercises 2776, find each product. (xy ab2)(xy ab2)
 5.4.5.1.484: In Exercises 2776, find each product. (x2 1)(x4y x2 1)
 5.4.5.1.485: In Exercises 2776, find each product. (x2 1)(xy4 y2 1)
 5.4.5.1.486: In Exercises 2776, find each product. (x2y2 3)2
 5.4.5.1.487: In Exercises 2776, find each product. (x2y2 5)2
 5.4.5.1.488: In Exercises 2776, find each product. (x y 1)(x y 1)
 5.4.5.1.489: In Exercises 2776, find each product. (x y 1)(x y 1)
 5.4.5.1.490: In Exercises 7780, write a polynomial in two variables thatdescribe...
 5.4.5.1.491: In Exercises 7780, write a polynomial in two variables thatdescribe...
 5.4.5.1.492: In Exercises 7780, write a polynomial in two variables thatdescribe...
 5.4.5.1.493: In Exercises 7780, write a polynomial in two variables thatdescribe...
 5.4.5.1.494: In Exercises 8186, find each product. As we said in the Section 5.3...
 5.4.5.1.495: In Exercises 8186, find each product. As we said in the Section 5.3...
 5.4.5.1.496: In Exercises 8186, find each product. As we said in the Section 5.3...
 5.4.5.1.497: In Exercises 8186, find each product. As we said in the Section 5.3...
 5.4.5.1.498: In Exercises 8186, find each product. As we said in the Section 5.3...
 5.4.5.1.499: In Exercises 8186, find each product. As we said in the Section 5.3...
 5.4.5.1.500: The number of board feet, N, that can be manufactured from a tree w...
 5.4.5.1.501: The storage shed shown in the figure has a volume given by the poly...
 5.4.5.1.502: How high above the ground will the ball be 2 seconds after being th...
 5.4.5.1.503: How high above the ground will the ball be 4 seconds after being th...
 5.4.5.1.504: How high above the ground will the ball be 6 seconds after being th...
 5.4.5.1.505: The graph visually displays the information about the thrown ball d...
 5.4.5.1.506: The graph visually displays the information about the thrown ball d...
 5.4.5.1.507: The graph visually displays the information about the thrown ball d...
 5.4.5.1.508: The graph visually displays the information about the thrown ball d...
 5.4.5.1.509: The graph visually displays the information about the thrown ball d...
 5.4.5.1.510: The graph visually displays the information about the thrown ball d...
 5.4.5.1.511: What is a polynomial in two variables? Provide an example with your...
 5.4.5.1.512: Explain how to find the degree of a polynomial in two variables.
 5.4.5.1.513: Suppose that you take up sky diving. Explain how to use the formula...
 5.4.5.1.514: In Exercises 101104, determine whether each statement makes sense o...
 5.4.5.1.515: In Exercises 101104, determine whether each statement makes sense o...
 5.4.5.1.516: In Exercises 101104, determine whether each statement makes sense o...
 5.4.5.1.517: In Exercises 101104, determine whether each statement makes sense o...
 5.4.5.1.518: In Exercises 105108, determine whether each statement is true or fa...
 5.4.5.1.519: In Exercises 105108, determine whether each statement is true or fa...
 5.4.5.1.520: In Exercises 105108, determine whether each statement is true or fa...
 5.4.5.1.521: In Exercises 105108, determine whether each statement is true or fa...
 5.4.5.1.522: In Exercises 109110, find a polynomial in two variables that descri...
 5.4.5.1.523: In Exercises 109110, find a polynomial in two variables that descri...
 5.4.5.1.524: Use the formulas for the volume of a rectangular solid and a cylind...
 5.4.5.1.525: Solve for W: R L 3W 2 . (Section 2.4, Example 4)
 5.4.5.1.526: Subtract: 6.4 (10.2). (Section 1.6, Example 2)
 5.4.5.1.527: Solve: 0.02(x 5) 0.03 0.03(x 7). (Section 2.3, Example 5)
 5.4.5.1.528: Exercises 115117 will help you prepare for the material covered in ...
 5.4.5.1.529: Exercises 115117 will help you prepare for the material covered in ...
 5.4.5.1.530: Exercises 115117 will help you prepare for the material covered in ...
Solutions for Chapter 5.4: Polynomials in Several Variables
Full solutions for Introductory & Intermediate Algebra for College Students  4th Edition
ISBN: 9780321758941
Solutions for Chapter 5.4: Polynomials in Several Variables
Get Full SolutionsIntroductory & Intermediate Algebra for College Students was written by and is associated to the ISBN: 9780321758941. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Introductory & Intermediate Algebra for College Students, edition: 4. Chapter 5.4: Polynomials in Several Variables includes 123 full stepbystep solutions. Since 123 problems in chapter 5.4: Polynomials in Several Variables have been answered, more than 71546 students have viewed full stepbystep solutions from this chapter.

Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

Cyclic shift
S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

Free variable Xi.
Column i has no pivot in elimination. We can give the n  r free variables any values, then Ax = b determines the r pivot variables (if solvable!).

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

Nilpotent matrix N.
Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

Sum V + W of subs paces.
Space of all (v in V) + (w in W). Direct sum: V n W = to}.

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.