 5.4.1: Fill in each blank with the correct response.In the term , the coef...
 5.4.2: Fill in each blank with the correct response.The expression has ter...
 5.4.3: Fill in each blank with the correct response.The degree of the term...
 5.4.4: Fill in each blank with the correct response.The polynomial an exam...
 5.4.5: Fill in each blank with the correct response.When is evaluated for ...
 5.4.6: Fill in each blank with the correct response.+ 3x3 5x  7x is a tri...
 5.4.7: Fill in each blank with the correct response.3xy  2xy + 5xy =
 5.4.8: Fill in each blank with the correct response.is an example of a mon...
 5.4.9: For each polynomial, determine the number of terms and name the coe...
 5.4.10: For each polynomial, determine the number of terms and name the coe...
 5.4.11: For each polynomial, determine the number of terms and name the coe...
 5.4.12: For each polynomial, determine the number of terms and name the coe...
 5.4.13: For each polynomial, determine the number of terms and name the coe...
 5.4.14: For each polynomial, determine the number of terms and name the coe...
 5.4.15: For each polynomial, determine the number of terms and name the coe...
 5.4.16: For each polynomial, determine the number of terms and name the coe...
 5.4.17: In each polynomial, add like terms whenever possible. Write the res...
 5.4.18: In each polynomial, add like terms whenever possible. Write the res...
 5.4.19: In each polynomial, add like terms whenever possible. Write the res...
 5.4.20: In each polynomial, add like terms whenever possible. Write the res...
 5.4.21: In each polynomial, add like terms whenever possible. Write the res...
 5.4.22: In each polynomial, add like terms whenever possible. Write the res...
 5.4.23: In each polynomial, add like terms whenever possible. Write the res...
 5.4.24: In each polynomial, add like terms whenever possible. Write the res...
 5.4.25: In each polynomial, add like terms whenever possible. Write the res...
 5.4.26: In each polynomial, add like terms whenever possible. Write the res...
 5.4.27: In each polynomial, add like terms whenever possible. Write the res...
 5.4.28: In each polynomial, add like terms whenever possible. Write the res...
 5.4.29: For each polynomial, first simplify, if possible, and write it in d...
 5.4.30: For each polynomial, first simplify, if possible, and write it in d...
 5.4.31: For each polynomial, first simplify, if possible, and write it in d...
 5.4.32: For each polynomial, first simplify, if possible, and write it in d...
 5.4.33: For each polynomial, first simplify, if possible, and write it in d...
 5.4.34: For each polynomial, first simplify, if possible, and write it in d...
 5.4.35: For each polynomial, first simplify, if possible, and write it in d...
 5.4.36: For each polynomial, first simplify, if possible, and write it in d...
 5.4.37: Find the value of each polynomial for (a) x = 2 and (b) . See Examp...
 5.4.38: Find the value of each polynomial for (a) x = 2 and (b) . See Examp...
 5.4.39: Find the value of each polynomial for (a) x = 2 and (b) . See Examp...
 5.4.40: Find the value of each polynomial for (a) x = 2 and (b) . See Examp...
 5.4.41: Find the value of each polynomial for (a) x = 2 and (b) . See Examp...
 5.4.42: Find the value of each polynomial for (a) x = 2 and (b) . See Examp...
 5.4.43: Add. See Example 5.3x  4y 2 + 2x3m2 5y +
 5.4.44: Add. See Example 5.8y  2m  4 3 33m2 5y + 5m + 6 3 2x + 3y
 5.4.45: Add. See Example 5.2m2 8y  2m 3m2 5y + 5m + 6
 5.4.46: Add. See Example 5.4a3  4a2  46a3 + 5a2  8
 5.4.47: Add. See Example 5.23 x2 + 15 x + 162 x2  13 x + 23
 5.4.48: Add. See Example 5.3 y2  13 y + 251347 y2  15 y + 79
 5.4.49: Add. See Example 5.9m3  5m2 + 4m  8 and 3m3 + 6m2  6
 5.4.50: Add. See Example 5.12r5 + 11r4  7r3  2r2 and 8r5 + 3r3 + 2r2
 5.4.51: Subtract. See Example 8.2y3 + 8y2 5y3  3y2
 5.4.52: Subtract. See Example 8.8t3  6t2 6t3 + 4t2
 5.4.53: Subtract. See Example 8.8x4 + 3x2  3x 12x4  x2 + x
 5.4.54: Subtract. See Example 8.7y5 + 5y3 + y2 13y5  y3  8y2
 5.4.55: Subtract. See Example 8.3m + a  1 3 + 5m2  5a4  3a3 + 2a2 12m 
 5.4.56: Subtract. See Example 8.6a4 + a3  a2 5a4  3a3 + 2a2
 5.4.57: After reading Examples 58, do you have a preference regarding horiz...
 5.4.58: Write a paragraph explaining how to add and subtract polynomials. G...
 5.4.59: Perform each indicated operation. See Examples 6 and 718m + 2 2  7...
 5.4.60: Perform each indicated operation. See Examples 6 and 71x2 + x2  13...
 5.4.61: Perform each indicated operation. See Examples 6 and 7116x3  x2 + ...
 5.4.62: Perform each indicated operation. See Examples 6 and 712b6 + 3b4 ...
 5.4.63: Perform each indicated operation. See Examples 6 and 7Subtract 18y4...
 5.4.64: Perform each indicated operation. See Examples 6 and 7Subtract 19t5...
 5.4.65: Perform each indicated operation. See Examples 6 and 719a4  3a2 + ...
 5.4.66: Perform each indicated operation. See Examples 6 and 714m2  3m + 2...
 5.4.67: Perform each indicated operation. See Examples 6 and 7318m2 + 4m  ...
 5.4.68: Perform each indicated operation. See Examples 6 and 7319b3  4b2 +...
 5.4.69: Perform each indicated operation. See Examples 6 and 7313x2  2x + ...
 5.4.70: Perform each indicated operation. See Examples 6 and 7316t2  3t + ...
 5.4.71: Without actually performing the operations, determine mentally the ...
 5.4.72: Without actually performing the operations, determine mentally the ...
 5.4.73: Add or subtract as indicated. See Example 9.16b + 3c2 + 12b  8c2
 5.4.74: Add or subtract as indicated. See Example 9.15t + 13s2 + 18t  3s2
 5.4.75: Add or subtract as indicated. See Example 9.14x + 2xy  32  12x +...
 5.4.76: Add or subtract as indicated. See Example 9.18ab + 2a  3b2  16ab ...
 5.4.77: Add or subtract as indicated. See Example 9.15x2y  2xy + 9xy22  1...
 5.4.78: Add or subtract as indicated. See Example 9.116t3s2 + 8t2s3 + 9ts42...
 5.4.79: Find a polynomial that represents the perimeter of each rectangle, ...
 5.4.80: Find a polynomial that represents the perimeter of each rectangle, ...
 5.4.81: Find a polynomial that represents the perimeter of each rectangle, ...
 5.4.82: Find a polynomial that represents the perimeter of each rectangle, ...
 5.4.83: Find a polynomial that represents the perimeter of each rectangle, ...
 5.4.84: Find a polynomial that represents the perimeter of each rectangle, ...
 5.4.85: Find (a) a polynomial that represents the perimeter of each triangl...
 5.4.86: Find (a) a polynomial that represents the perimeter of each triangl...
 5.4.87: Perform each indicated operation.Find the difference between the su...
 5.4.88: Perform each indicated operation.Subtract the sum of 9t  8t + 4 3 ...
 5.4.89: Graph each equation by completing the table of values. See Example ...
 5.4.90: Graph each equation by completing the table of values. See Example ...
 5.4.91: Graph each equation by completing the table of values. See Example ...
 5.4.92: Graph each equation by completing the table of values. See Example ...
 5.4.93: Graph each equation by completing the table of values. See Example ...
 5.4.94: Graph each equation by completing the table of values. See Example ...
 5.4.95: Graph each equation by completing the table of values. See Example ...
 5.4.96: Graph each equation by completing the table of values. See Example ...
 5.4.97: The polynomial equation y = 0.0545x2 + 5.047x + 11.78gives a good ...
 5.4.98: The polynomial equation y = 0.0545x2 + 5.047x + 11.78gives a good ...
 5.4.99: The polynomial equation y = 0.0545x2 + 5.047x + 11.78gives a good ...
 5.4.100: The polynomial equation y = 0.0545x2 + 5.047x + 11.78gives a good ...
 5.4.101: Multiply. See Section 1.851x + 42
 5.4.102: Multiply. See Section 1.831x 2 + 72
 5.4.103: Multiply. See Section 1.8412a + 6b2
 5.4.104: Multiply. See Section 1.812 4m  8n2
 5.4.105: Multiply. See Section 5.1.12a215ab2
 5.4.106: Multiply. See Section 5.1.13xz214x2
 5.4.107: Multiply. See Section 5.1.1m 2 221m5
 5.4.108: Multiply. See Section 5.1.12c213c2 1m 2
Solutions for Chapter 5.4: Adding and Subtracting Polynomials; Graphing Simple Polynomials
Full solutions for Beginning Algebra  11th Edition
ISBN: 9780321673480
Solutions for Chapter 5.4: Adding and Subtracting Polynomials; Graphing Simple Polynomials
Get Full SolutionsThis textbook survival guide was created for the textbook: Beginning Algebra, edition: 11. Since 108 problems in chapter 5.4: Adding and Subtracting Polynomials; Graphing Simple Polynomials have been answered, more than 37795 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 5.4: Adding and Subtracting Polynomials; Graphing Simple Polynomials includes 108 full stepbystep solutions. Beginning Algebra was written by and is associated to the ISBN: 9780321673480.

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

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (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.

Dimension of vector space
dim(V) = number of vectors in any basis for V.

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

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

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

Iterative method.
A sequence of steps intended to approach the desired solution.

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

Nullspace matrix N.
The columns of N are the n  r special solutions to As = O.

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

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

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

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

Rotation matrix
R = [~ CS ] rotates the plane by () and R 1 = RT rotates back by (). Eigenvalues are eiO and eiO , eigenvectors are (1, ±i). c, s = cos (), sin ().

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).