 6.4.1: Divide. See Examples 1 and 2.4a2 + 8a by 2a
 6.4.2: Divide. See Examples 1 and 2.6x4  3x3 by 3x2
 6.4.3: Divide. See Examples 1 and 2.12a5b2 + 16a4b4a4b
 6.4.4: Divide. See Examples 1 and 2.4x3y + 12x2y2  4xy34xy
 6.4.5: Divide. See Examples 1 and 2.4x2y2 + 6xy2  4y22x2y
 6.4.6: Divide. See Examples 1 and 2.6x5y + 75x4y  24x3y23x4y
 6.4.7: Divide. See Examples 3 through 7.1x2 + 3x + 22 , 1x + 22
 6.4.8: Divide. See Examples 3 through 7.1y2 + 7y + 102 , 1y + 52
 6.4.9: Divide. See Examples 3 through 7.12x2  6x  82 , 1x + 12
 6.4.10: Divide. See Examples 3 through 7.13x2 + 19x + 202 , 1x + 52
 6.4.11: Divide. See Examples 3 through 7.2x2 + 3x  2 by 2x + 4
 6.4.12: Divide. See Examples 3 through 7.6x2  17x  3 by 3x  9
 6.4.13: Divide. See Examples 3 through 7.14x3 + 7x2 + 8x + 202 , 12x + 42
 6.4.14: Divide. See Examples 3 through 7.18x3 + 18x2 + 16x + 242 , 14x + 82
 6.4.15: Divide. See Examples 3 through 7.12x2 + 6x3  18x  62 , 13x + 12
 6.4.16: Divide. See Examples 3 through 7.14x  15x2 + 10x3  62 , 12x  32
 6.4.17: Divide. See Examples 3 through 7.13x5  x3 + 4x2  12x  82 , 1x2  22
 6.4.18: Divide. See Examples 3 through 7.12x5  6x4 + x3  4x + 32 , 1x2  32
 6.4.19: Divide. See Examples 3 through 7. a2x4 +12x3 + x2 + xb , 1x  22
 6.4.20: Divide. See Examples 3 through 7.ax4  23x3 + xb , 1x  32
 6.4.21: Use synthetic division to divide. See Examples 8 and 9.x2 + 3x  40...
 6.4.22: Use synthetic division to divide. See Examples 8 and 9.x2  14x + 2...
 6.4.23: Use synthetic division to divide. See Examples 8 and 9.x2 + 5x  6x...
 6.4.24: Use synthetic division to divide. See Examples 8 and 9.x2 + 12x + 3...
 6.4.25: Use synthetic division to divide. See Examples 8 and 9.x3  7x2  1...
 6.4.26: Use synthetic division to divide. See Examples 8 and 9.x3 + 6x2 + 4...
 6.4.27: Use synthetic division to divide. See Examples 8 and 9.4x2  9x  2
 6.4.28: Use synthetic division to divide. See Examples 8 and 9.3x2  4x  1
 6.4.29: Divide. See Examples 1 9.4x7y4 + 8xy2 + 4xy34xy3
 6.4.30: Divide. See Examples 1 9.15x3y  5x2y + 10xy25x2y
 6.4.31: Divide. See Examples 1 9.110x3  5x2  12x + 12 , 12x  12
 6.4.32: Divide. See Examples 1 9.120x3  8x2 + 5x  52 , 15x  22
 6.4.33: Divide. See Examples 1 9.12x3  6x2  42 , 1x  42
 6.4.34: Divide. See Examples 1 9.13x3 + 4x  102 , 1x + 22
 6.4.35: Divide. See Examples 1 9.2x4  13x3 + 16x2  9x + 20x  5
 6.4.36: Divide. See Examples 1 9.3x4 + 5x3  x2 + x  2x + 2
 6.4.37: Divide. See Examples 1 9.7x2  4x + 12 + 3x3x + 1
 6.4.38: Divide. See Examples 1 9.4x3 + x4  x2  16x  4x  2
 6.4.39: Divide. See Examples 1 9.3x3 + 2x2  4x + 1x  13
 6.4.40: Divide. See Examples 1 9.9y3 + 9y2  y + 2y +23
 6.4.41: Divide. See Examples 1 9.x3  1x  1
 6.4.42: Divide. See Examples 1 9.y3  8y  2
 6.4.43: Divide. See Examples 1 9.125xy2 + 75xyz + 125x2yz2 , 1 5x2y2
 6.4.44: Divide. See Examples 1 9.1x6y6  x3y3z + 7x3y2 , 1 7yz22
 6.4.45: Divide. See Examples 1 9.19x5 + 6x4  6x2  4x2 , 13x + 22
 6.4.46: Divide. See Examples 1 9.15x4  5x2 + 10x3  10x2 , 15x + 102
 6.4.47: For the given polynomial P1x2 and the given c, use the remainder th...
 6.4.48: For the given polynomial P1x2 and the given c, use the remainder th...
 6.4.49: For the given polynomial P1x2 and the given c, use the remainder th...
 6.4.50: For the given polynomial P1x2 and the given c, use the remainder th...
 6.4.51: For the given polynomial P1x2 and the given c, use the remainder th...
 6.4.52: For the given polynomial P1x2 and the given c, use the remainder th...
 6.4.53: For the given polynomial P1x2 and the given c, use the remainder th...
 6.4.54: For the given polynomial P1x2 and the given c, use the remainder th...
 6.4.55: For the given polynomial P1x2 and the given c, use the remainder th...
 6.4.56: For the given polynomial P1x2 and the given c, use the remainder th...
 6.4.57: Solve each equation for x. See Sections 2.1 and 5.8.7x + 2 = x  3
 6.4.58: Solve each equation for x. See Sections 2.1 and 5.8.4  2x = 17  5x
 6.4.59: Solve each equation for x. See Sections 2.1 and 5.8.x2 = 4x  4
 6.4.60: Solve each equation for x. See Sections 2.1 and 5.8.5x2 + 10x = 15
 6.4.61: Solve each equation for x. See Sections 2.1 and 5.8.x3  5 = 13
 6.4.62: Solve each equation for x. See Sections 2.1 and 5.8.2x9+ 1 = 79
 6.4.63: Factor the following. See Sections 5.5 and 5.7.x3  1
 6.4.64: Factor the following. See Sections 5.5 and 5.7.8y3 + 1
 6.4.65: Factor the following. See Sections 5.5 and 5.7.125z3 + 8
 6.4.66: Factor the following. See Sections 5.5 and 5.7.a3  27
 6.4.67: Factor the following. See Sections 5.5 and 5.7.xy + 2x + 3y + 6
 6.4.68: Factor the following. See Sections 5.5 and 5.7.x2  x + xy  y
 6.4.69: Factor the following. See Sections 5.5 and 5.7.x3  9x
 6.4.70: Factor the following. See Sections 5.5 and 5.7.2x3  32x
 6.4.71: Determine whether each division problem is a candidate for the synt...
 6.4.72: Determine whether each division problem is a candidate for the synt...
 6.4.73: Determine whether each division problem is a candidate for the synt...
 6.4.74: Determine whether each division problem is a candidate for the synt...
 6.4.75: In a long division exercise, if the divisor is 9x3  2x, the divisi...
 6.4.76: In a division exercise, if the divisor is x  3, the division proce...
 6.4.77: A board of length 13x4 + 6x2  182 meters is to be cut into three p...
 6.4.78: The perimeter of a regular hexagon is given to be 112x5  48x3 + 32...
 6.4.79: If the area of the rectangle is 115x2  29x  142 square inches, an...
 6.4.80: If the area of a parallelogram is 12x2  17x + 352 square centimete...
 6.4.81: If the area of a parallelogram is 1x4  23x2 + 9x  52 square centi...
 6.4.82: If the volume of a box is 1x4 + 6x3  7x2 2 cubic meters, its heigh...
 6.4.83: Divide.ax4 +23x3 + xb , 1x  12
 6.4.84: Divide. a2x3 +92x2  4x  10b , 1x + 22
 6.4.85: Divide.a3x4  x  x3 +12b , 12x  12
 6.4.86: Divide.a2x4 +12x3  14x2 + xb , 12x + 12
 6.4.87: Divide.15x4  2x2 + 10x3  4x2 , 15x + 102
 6.4.88: Divide.19x5 + 6x4  6x2  4x2 , 13x + 22
 6.4.89: For each given f(x) and g(x), find f 1x2 g1x2 . Also find any xval...
 6.4.90: For each given f(x) and g(x), find f 1x2 g1x2 . Also find any xval...
 6.4.91: For each given f(x) and g(x), find f 1x2 g1x2 . Also find any xval...
 6.4.92: For each given f(x) and g(x), find f 1x2 g1x2 . Also find any xval...
 6.4.93: Try performing the following division without changing theorder of ...
 6.4.94: Explain how to check polynomial long division.
 6.4.95: Explain an advantage of using the remainder theorem instead of dire...
 6.4.96: Explain an advantage of using synthetic division instead of long di...
 6.4.97: We say that 2 is a factor of 8 because 2 divides 8 evenly, or with ...
 6.4.98: We say that 2 is a factor of 8 because 2 divides 8 evenly, or with ...
 6.4.99: We say that 2 is a factor of 8 because 2 divides 8 evenly, or with ...
 6.4.100: We say that 2 is a factor of 8 because 2 divides 8 evenly, or with ...
 6.4.101: eBay is the leading online auction house. eBays annual net profit c...
 6.4.102: Kraft Foods is a provider of many of the bestknownfood brands in o...
 6.4.103: From the remainder theorem, the polynomial x  c is a factorof a po...
Solutions for Chapter 6.4: Dividing Polynomials: Long Division and Synthetic Division
Full solutions for Intermediate Algebra  6th Edition
ISBN: 9780321785046
Solutions for Chapter 6.4: Dividing Polynomials: Long Division and Synthetic Division
Get Full SolutionsThis textbook survival guide was created for the textbook: Intermediate Algebra, edition: 6. Chapter 6.4: Dividing Polynomials: Long Division and Synthetic Division includes 103 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 103 problems in chapter 6.4: Dividing Polynomials: Long Division and Synthetic Division have been answered, more than 60245 students have viewed full stepbystep solutions from this chapter. Intermediate Algebra was written by and is associated to the ISBN: 9780321785046.

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).

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

Basis for V.
Independent vectors VI, ... , v d whose linear combinations give each vector in V as v = CIVI + ... + CdVd. V has many bases, each basis gives unique c's. A vector space has many bases!

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

Matrix multiplication AB.
The i, j entry of AB is (row i of A)·(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

Row picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·

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

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.