 5.1.5.1.1: Fill in each blank so that the resulting statement is true. A polyn...
 5.1.5.1.2: Fill in each blank so that the resulting statement is true. It is c...
 5.1.5.1.3: Fill in each blank so that the resulting statement is true. A simpl...
 5.1.5.1.4: Fill in each blank so that the resulting statement is true. A simpl...
 5.1.5.1.5: Fill in each blank so that the resulting statement is true. A simpl...
 5.1.5.1.6: Fill in each blank so that the resulting statement is true. The deg...
 5.1.5.1.7: Fill in each blank so that the resulting statement is true. The deg...
 5.1.5.1.8: Fill in each blank so that the resulting statement is true. Polynom...
 5.1.5.1.9: Fill in each blank so that the resulting statement is true. To subt...
 5.1.5.1.10: In Exercises 116, identify each polynomial as a monomial, a binomia...
 5.1.5.1.11: In Exercises 116, identify each polynomial as a monomial, a binomia...
 5.1.5.1.12: In Exercises 116, identify each polynomial as a monomial, a binomia...
 5.1.5.1.13: In Exercises 116, identify each polynomial as a monomial, a binomia...
 5.1.5.1.14: In Exercises 116, identify each polynomial as a monomial, a binomia...
 5.1.5.1.15: In Exercises 116, identify each polynomial as a monomial, a binomia...
 5.1.5.1.16: In Exercises 116, identify each polynomial as a monomial, a binomia...
 5.1.5.1.17: In Exercises 116, identify each polynomial as a monomial, a binomia...
 5.1.5.1.18: In Exercises 116, identify each polynomial as a monomial, a binomia...
 5.1.5.1.19: In Exercises 116, identify each polynomial as a monomial, a binomia...
 5.1.5.1.20: In Exercises 116, identify each polynomial as a monomial, a binomia...
 5.1.5.1.21: In Exercises 116, identify each polynomial as a monomial, a binomia...
 5.1.5.1.22: In Exercises 116, identify each polynomial as a monomial, a binomia...
 5.1.5.1.23: In Exercises 116, identify each polynomial as a monomial, a binomia...
 5.1.5.1.24: In Exercises 116, identify each polynomial as a monomial, a binomia...
 5.1.5.1.25: In Exercises 116, identify each polynomial as a monomial, a binomia...
 5.1.5.1.26: In Exercises 1738, add the polynomials. (9x 8) (17x 5)
 5.1.5.1.27: In Exercises 1738, add the polynomials. (8x 5) (13x 9)
 5.1.5.1.28: In Exercises 1738, add the polynomials. (4x2 6x 7) (8x2 9x 2)
 5.1.5.1.29: In Exercises 1738, add the polynomials. (11x2 7x 4) (27x2 10x 20)
 5.1.5.1.30: In Exercises 1738, add the polynomials. (7x2 11x) (3x2 x)
 5.1.5.1.31: In Exercises 1738, add the polynomials. (3x2 x) (4x2 8x)
 5.1.5.1.32: In Exercises 1738, add the polynomials. (4x2 6x 12) (x2 3x 1)
 5.1.5.1.33: In Exercises 1738, add the polynomials. (7x2 8x 3) (2x2 x 8)
 5.1.5.1.34: In Exercises 1738, add the polynomials. (4y3 7y 5) (10y2 6y 3)
 5.1.5.1.35: In Exercises 1738, add the polynomials. (2y3 3y 10) (3y2 5y 22)
 5.1.5.1.36: In Exercises 1738, add the polynomials. (2x2 6x 7) (3x3 3x)
 5.1.5.1.37: In Exercises 1738, add the polynomials. (4x3 5x 13) (4x2 22)
 5.1.5.1.38: In Exercises 1738, add the polynomials. (4y2 8y 11) (2y3 5y 2)
 5.1.5.1.39: In Exercises 1738, add the polynomials. (7y3 5y 1) (2y2 6y 3)
 5.1.5.1.40: In Exercises 1738, add the polynomials. (2y6 3y4 y2) (y6 5y4 2y2)
 5.1.5.1.41: In Exercises 1738, add the polynomials. (7r4 5r2 2r) (18r4 5r2 r)
 5.1.5.1.42: In Exercises 1738, add the polynomials. 9x3 x2 x 1 3 x3 x2 x 4 3
 5.1.5.1.43: In Exercises 1738, add the polynomials. 12x3 x2 x 4 3 x3 x2 x 1 3
 5.1.5.1.44: In Exercises 1738, add the polynomials. 1 5 x4 1 3 x3 3 8 x2 6 3 5 ...
 5.1.5.1.45: In Exercises 1738, add the polynomials. 2 5 x4 2 3 x3 5 8 x2 7 4 5 ...
 5.1.5.1.46: In Exercises 1738, add the polynomials. (0.03x5 0.1x3 x 0.03) (0.02...
 5.1.5.1.47: In Exercises 1738, add the polynomials. (0.06x5 0.2x3 x 0.05) (0.04...
 5.1.5.1.48: In Exercises 3954, use a vertical format to add the polynomials 5y3...
 5.1.5.1.49: In Exercises 3954, use a vertical format to add the polynomials 13x...
 5.1.5.1.50: In Exercises 3954, use a vertical format to add the polynomials 3x2...
 5.1.5.1.51: In Exercises 3954, use a vertical format to add the polynomials 7x2...
 5.1.5.1.52: In Exercises 3954, use a vertical format to add the polynomials 14 ...
 5.1.5.1.53: In Exercises 3954, use a vertical format to add the polynomials 13 ...
 5.1.5.1.54: In Exercises 3954, use a vertical format to add the polynomials y3 ...
 5.1.5.1.55: In Exercises 3954, use a vertical format to add the polynomials y3 ...
 5.1.5.1.56: In Exercises 3954, use a vertical format to add the polynomials 4x3...
 5.1.5.1.57: In Exercises 3954, use a vertical format to add the polynomials 4y3...
 5.1.5.1.58: In Exercises 3954, use a vertical format to add the polynomials 7x4...
 5.1.5.1.59: In Exercises 3954, use a vertical format to add the polynomials 7y5...
 5.1.5.1.60: In Exercises 3954, use a vertical format to add the polynomials 7x2...
 5.1.5.1.61: In Exercises 3954, use a vertical format to add the polynomials 7y2...
 5.1.5.1.62: In Exercises 3954, use a vertical format to add the polynomials 1.2...
 5.1.5.1.63: In Exercises 3954, use a vertical format to add the polynomials 7.9...
 5.1.5.1.64: In Exercises 5574, subtract the polynomials (x 8) (3x 2)
 5.1.5.1.65: In Exercises 5574, subtract the polynomials (x 2) (7x 9)
 5.1.5.1.66: In Exercises 5574, subtract the polynomials (x2 5x 3) (6x2 4x 9)
 5.1.5.1.67: In Exercises 5574, subtract the polynomials (3x2 8x 2) (11x2 5x 4)
 5.1.5.1.68: In Exercises 5574, subtract the polynomials (x2 5x) (6x2 4x)
 5.1.5.1.69: In Exercises 5574, subtract the polynomials (3x2 2x) (5x2 6x)
 5.1.5.1.70: In Exercises 5574, subtract the polynomials (x2 8x 9) (5x2 4x 3)
 5.1.5.1.71: In Exercises 5574, subtract the polynomials (x2 5x 3) (x2 6x 8)
 5.1.5.1.72: In Exercises 5574, subtract the polynomials (y 8) (3y 2)
 5.1.5.1.73: In Exercises 5574, subtract the polynomials (y 2) (7y 9)
 5.1.5.1.74: In Exercises 5574, subtract the polynomials (6y3 2y2 y 11) (y2 8y 9)
 5.1.5.1.75: In Exercises 5574, subtract the polynomials (5y3 y2 3y 8) (y2 8y 11)
 5.1.5.1.76: In Exercises 5574, subtract the polynomials (7n3 n7 8) (6n3 n7 10)
 5.1.5.1.77: In Exercises 5574, subtract the polynomials (2n2 n7 6) (2n3 n7 8)
 5.1.5.1.78: In Exercises 5574, subtract the polynomials (y6 y3) (y2 y)
 5.1.5.1.79: In Exercises 5574, subtract the polynomials (y5 y3) (y4 y2)
 5.1.5.1.80: In Exercises 5574, subtract the polynomials (7x4 4x2 5x) (19x4 5x2 x)
 5.1.5.1.81: In Exercises 5574, subtract the polynomials (3x6 3x4 x2) (x6 2x4 2x2)
 5.1.5.1.82: In Exercises 5574, subtract the polynomials 3 7 x3 1 5 x 1 3 2 7 x3...
 5.1.5.1.83: In Exercises 5574, subtract the polynomials 3 8 x2 1 3 x 1 4 1 8 x2...
 5.1.5.1.84: In Exercises 7588, use a vertical format to subtract the polynomial...
 5.1.5.1.85: In Exercises 7588, use a vertical format to subtract the polynomial...
 5.1.5.1.86: In Exercises 7588, use a vertical format to subtract the polynomial...
 5.1.5.1.87: In Exercises 7588, use a vertical format to subtract the polynomial...
 5.1.5.1.88: In Exercises 7588, use a vertical format to subtract the polynomial...
 5.1.5.1.89: In Exercises 7588, use a vertical format to subtract the polynomial...
 5.1.5.1.90: In Exercises 7588, use a vertical format to subtract the polynomial...
 5.1.5.1.91: In Exercises 7588, use a vertical format to subtract the polynomial...
 5.1.5.1.92: In Exercises 7588, use a vertical format to subtract the polynomial...
 5.1.5.1.93: In Exercises 7588, use a vertical format to subtract the polynomial...
 5.1.5.1.94: In Exercises 7588, use a vertical format to subtract the polynomial...
 5.1.5.1.95: In Exercises 7588, use a vertical format to subtract the polynomial...
 5.1.5.1.96: In Exercises 7588, use a vertical format to subtract the polynomial...
 5.1.5.1.97: In Exercises 7588, use a vertical format to subtract the polynomial...
 5.1.5.1.98: Graph each equation in Exercises 8994. Find seven solutions in your...
 5.1.5.1.99: Graph each equation in Exercises 8994. Find seven solutions in your...
 5.1.5.1.100: Graph each equation in Exercises 8994. Find seven solutions in your...
 5.1.5.1.101: Graph each equation in Exercises 8994. Find seven solutions in your...
 5.1.5.1.102: Graph each equation in Exercises 8994. Find seven solutions in your...
 5.1.5.1.103: Graph each equation in Exercises 8994. Find seven solutions in your...
 5.1.5.1.104: In Exercises 9598, perform the indicated operations. (4x2 7x 5) (2x...
 5.1.5.1.105: In Exercises 9598, perform the indicated operations. (10x3 5x2 4x 3...
 5.1.5.1.106: In Exercises 9598, perform the indicated operations. (4y2 3y 8) (5y...
 5.1.5.1.107: In Exercises 9598, perform the indicated operations. (7y2 4y 2) (12...
 5.1.5.1.108: Subtract x3 2x2 2 from the sum of 4x3 x2 and x3 7x 3.
 5.1.5.1.109: Subtract 3x3 7x 5 from the sum of 2x2 4x 7 and 5x3 2x 3.
 5.1.5.1.110: Subtract y2 7y3 from the difference between 5 y2 4y3 and 8 y 7y3. E...
 5.1.5.1.111: Subtract 2y2 8y3 from the difference between 6 y2 5y3 and 12 y 13y3...
 5.1.5.1.112: Exercises 103106 are based on these models and the data displayed b...
 5.1.5.1.113: Exercises 103106 are based on these models and the data displayed b...
 5.1.5.1.114: Exercises 103106 are based on these models and the data displayed b...
 5.1.5.1.115: Exercises 103106 are based on these models and the data displayed b...
 5.1.5.1.116: What is a polynomial?
 5.1.5.1.117: What is a monomial? Give an example with your explanation.
 5.1.5.1.118: What is a binomial? Give an example with your explanation.
 5.1.5.1.119: What is a trinomial? Give an example with your explanation.
 5.1.5.1.120: What is the degree of a polynomial? Provide an example with your ex...
 5.1.5.1.121: Explain how to add polynomials.
 5.1.5.1.122: Explain how to subtract polynomials.
 5.1.5.1.123: In Exercises 114117, determine whether each statement makes sense o...
 5.1.5.1.124: In Exercises 114117, determine whether each statement makes sense o...
 5.1.5.1.125: In Exercises 114117, determine whether each statement makes sense o...
 5.1.5.1.126: In Exercises 114117, determine whether each statement makes sense o...
 5.1.5.1.127: In Exercises 118121, determine whether each statement is true or fa...
 5.1.5.1.128: In Exercises 118121, determine whether each statement is true or fa...
 5.1.5.1.129: In Exercises 118121, determine whether each statement is true or fa...
 5.1.5.1.130: In Exercises 118121, determine whether each statement is true or fa...
 5.1.5.1.131: What polynomial must be subtracted from 5x2 2x 1 so that the differ...
 5.1.5.1.132: The number of people who catch a cold t weeks after January 1 is 5t...
 5.1.5.1.133: Explain why it is not possible to add two polynomials of degree 3 a...
 5.1.5.1.134: Simplify: (10)(7) (1 8). (Section 1.8, Example 8)
 5.1.5.1.135: Subtract: 4.6 (10.2). (Section 1.6, Example 2)
 5.1.5.1.136: Solve: 3(x 2) 9(x 2). (Section 2.3, Example 3)
 5.1.5.1.137: Exercises 128130 will help you prepare for the material covered in ...
 5.1.5.1.138: Exercises 128130 will help you prepare for the material covered in ...
 5.1.5.1.139: Exercises 128130 will help you prepare for the material covered in ...
Solutions for Chapter 5.1: Adding and Subtracting Polynomials
Full solutions for Introductory & Intermediate Algebra for College Students  4th Edition
ISBN: 9780321758941
Solutions for Chapter 5.1: Adding and Subtracting Polynomials
Get Full SolutionsChapter 5.1: Adding and Subtracting Polynomials includes 139 full stepbystep solutions. Since 139 problems in chapter 5.1: Adding and Subtracting Polynomials have been answered, more than 75376 students have viewed full stepbystep solutions from this chapter. Introductory & Intermediate Algebra for College Students was written by and is associated to the ISBN: 9780321758941. This textbook survival guide was created for the textbook: Introductory & Intermediate Algebra for College Students, edition: 4. This expansive textbook survival guide covers the following chapters and their solutions.

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.

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

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

Determinant IAI = det(A).
Defined by det I = 1, sign reversal for row exchange, and linearity in each row. Then IAI = 0 when A is singular. Also IABI = IAIIBI and

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

Matrix multiplication AB.
The i, j entry of AB is (row i of A)ยท(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 .

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).

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

Orthogonal matrix Q.
Square matrix with orthonormal columns, so QT = Ql. Preserves length and angles, IIQxll = IIxll and (QX)T(Qy) = xTy. AlllAI = 1, with orthogonal eigenvectors. Examples: Rotation, reflection, permutation.

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

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

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

Singular Value Decomposition
(SVD) A = U:E VT = (orthogonal) ( diag)( orthogonal) First r columns of U and V are orthonormal bases of C (A) and C (AT), AVi = O'iUi with singular value O'i > O. Last columns are orthonormal bases of nullspaces.

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

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.