 5.3.1: Find the degree of each term. See Example 1.4
 5.3.2: Find the degree of each term. See Example 1.7
 5.3.3: Find the degree of each term. See Example 1.5x2
 5.3.4: Find the degree of each term. See Example 1.z3
 5.3.5: Find the degree of each term. See Example 1.3xy2
 5.3.6: Find the degree of each term. See Example 1.12x3z
 5.3.7: Find the degree of each term. See Example 1.87y3
 5.3.8: Find the degree of each term. See Example 1.911y5
 5.3.9: Find the degree of each term. See Example 1.3.78ab3c 5
 5.3.10: Find the degree of each term. See Example 1.9.11r2st 12
 5.3.11: Find the degree of each polynomial and indicate whether the polynom...
 5.3.12: Find the degree of each polynomial and indicate whether the polynom...
 5.3.13: Find the degree of each polynomial and indicate whether the polynom...
 5.3.14: Find the degree of each polynomial and indicate whether the polynom...
 5.3.15: Find the degree of each polynomial and indicate whether the polynom...
 5.3.16: Find the degree of each polynomial and indicate whether the polynom...
 5.3.17: Find the degree of each polynomial and indicate whether the polynom...
 5.3.18: Find the degree of each polynomial and indicate whether the polynom...
 5.3.19: If P1x2 = x2 + x + 1 and Q1x2 = 5x2  1, find the following. See Ex...
 5.3.20: If P1x2 = x2 + x + 1 and Q1x2 = 5x2  1, find the following. See Ex...
 5.3.21: If P1x2 = x2 + x + 1 and Q1x2 = 5x2  1, find the following. See Ex...
 5.3.22: If P1x2 = x2 + x + 1 and Q1x2 = 5x2  1, find the following. See Ex...
 5.3.23: If P1x2 = x2 + x + 1 and Q1x2 = 5x2  1, find the following. See Ex...
 5.3.24: If P1x2 = x2 + x + 1 and Q1x2 = 5x2  1, find the following. See Ex...
 5.3.25: Refer to Example 5 for Exercises 25 through 28.Find the height of t...
 5.3.26: Refer to Example 5 for Exercises 25 through 28.Find the height of t...
 5.3.27: Refer to Example 5 for Exercises 25 through 28.Find the height of t...
 5.3.28: Refer to Example 5 for Exercises 25 through 28.Approximate (to the ...
 5.3.29: Simplify each polynomial by combining like terms. See Example 6.5y ...
 5.3.30: Simplify each polynomial by combining like terms. See Example 6.x ...
 5.3.31: Simplify each polynomial by combining like terms. See Example 6.4x2...
 5.3.32: Simplify each polynomial by combining like terms. See Example 6.8x...
 5.3.33: Simplify each polynomial by combining like terms. See Example 6.7x2...
 5.3.34: Simplify each polynomial by combining like terms. See Example 6.a2...
 5.3.35: Add. See Examples 7 and 8.19y2 + y  82 + 19y2  y  92
 5.3.36: Add. See Examples 7 and 8.1x2 + 4x  72 + 18x2 + 9x  72
 5.3.37: Add. See Examples 7 and 8.1x2 + xy  y22 and 12x2  4xy + 7y22
 5.3.38: Add. See Examples 7 and 8.16x2 + 5x + 72 and 1x2 + 6x  32
 5.3.39: Add. See Examples 7 and 8.x2  6x + 3+ 12x + 52
 5.3.40: Add. See Examples 7 and 8.2x2 + 3x  9+ 12x  32
 5.3.41: Add. See Examples 7 and 8.17x3y  4xy + 82 + 15x3y + 4xy + 8x2
 5.3.42: Add. See Examples 7 and 8.19xyz + 4x  y2 + 1 9xyz  3x + y + 22
 5.3.43: Add. See Examples 7 and 8.10.6x3 + 1.2x2  4.5x + 9.12 + 13.9x3  x...
 5.3.44: Add. See Examples 7 and 8.19.3y2  y + 12.82 + 12.6y2 + 4.4y  8.92
 5.3.45: Subtract. See Examples 9 and 10.19y2  7y + 52  18y2  7y + 22
 5.3.46: Subtract. See Examples 9 and 10.12x2 + 3x + 122  120x2  5x  72
 5.3.47: Subtract. See Examples 9 and 10.Subtract 16x2  3x2 from 14x2 + 2x2.
 5.3.48: Subtract. See Examples 9 and 10.Subtract 18y2 + 4x2 from 1y2 + x2.
 5.3.49: Subtract. See Examples 9 and 10.6y2  6y + 41 y2 + 6y + 72
 5.3.50: Subtract. See Examples 9 and 10.4x3 + 4x2  4x12x3  2x2 + 3x2
 5.3.51: Subtract. See Examples 9 and 10.19x3  2x2 + 4x  72  12x3  6x2 ...
 5.3.52: Subtract. See Examples 9 and 10.13x2 + 6xy + 3y22  18x2  6xy  y22
 5.3.53: Subtract. See Examples 9 and 10.Subtract ay2 + 4yx +17b from a 19y...
 5.3.54: Subtract. See Examples 9 and 10.Subtract a13x2 + x2y  14b from a3x...
 5.3.55: Perform indicated operations and simplify. See Examples 6 through 1...
 5.3.56: Perform indicated operations and simplify. See Examples 6 through 1...
 5.3.57: Perform indicated operations and simplify. See Examples 6 through 1...
 5.3.58: Perform indicated operations and simplify. See Examples 6 through 1...
 5.3.59: Perform indicated operations and simplify. See Examples 6 through 1...
 5.3.60: Perform indicated operations and simplify. See Examples 6 through 1...
 5.3.61: Perform indicated operations and simplify. See Examples 6 through 1...
 5.3.62: Perform indicated operations and simplify. See Examples 6 through 1...
 5.3.63: Perform indicated operations and simplify. See Examples 6 through 1...
 5.3.64: Perform indicated operations and simplify. See Examples 6 through 1...
 5.3.65: Perform indicated operations and simplify. See Examples 6 through 1...
 5.3.66: Perform indicated operations and simplify. See Examples 6 through 1...
 5.3.67: Perform indicated operations and simplify. See Examples 6 through 1...
 5.3.68: Perform indicated operations and simplify. See Examples 6 through 1...
 5.3.69: Perform indicated operations and simplify. See Examples 6 through 1...
 5.3.70: Perform indicated operations and simplify. See Examples 6 through 1...
 5.3.71: Perform indicated operations and simplify. See Examples 6 through 1...
 5.3.72: Perform indicated operations and simplify. See Examples 6 through 1...
 5.3.73: Perform indicated operations and simplify. See Examples 6 through 1...
 5.3.74: Perform indicated operations and simplify. See Examples 6 through 1...
 5.3.75: Perform indicated operations and simplify. See Examples 6 through 1...
 5.3.76: Perform indicated operations and simplify. See Examples 6 through 1...
 5.3.77: Perform indicated operations and simplify. See Examples 6 through 1...
 5.3.78: Perform indicated operations and simplify. See Examples 6 through 1...
 5.3.79: Perform indicated operations and simplify. See Examples 6 through 1...
 5.3.80: Perform indicated operations and simplify. See Examples 6 through 1...
 5.3.81: Use the information below to solve Exercises 81 and 82. The surface...
 5.3.82: Use the information below to solve Exercises 81 and 82. The surface...
 5.3.83: Use the information below to solve Exercises 81 and 82. The surface...
 5.3.84: Use the information below to solve Exercises 81 and 82. The surface...
 5.3.85: Use the information below to solve Exercises 81 and 82. The surface...
 5.3.86: Use the information below to solve Exercises 81 and 82. The surface...
 5.3.87: Use the information below to solve Exercises 81 and 82. The surface...
 5.3.88: Use the information below to solve Exercises 81 and 82. The surface...
 5.3.89: Match each equation with its graph. See Example 11.f 1x2 = 3x2  2
 5.3.90: Match each equation with its graph. See Example 11. h1x2 = 5x3  6x...
 5.3.91: Match each equation with its graph. See Example 11.g1x2 = 2x3  3x...
 5.3.92: Match each equation with its graph. See Example 11.F1x2 = 2x2  6x...
 5.3.93: Multiply. See Section 1.4.513x  22
 5.3.94: Multiply. See Section 1.4.712z  6y2
 5.3.95: Multiply. See Section 1.4.21x2  5x + 62
 5.3.96: Multiply. See Section 1.4.51 3y2  2y + 72
 5.3.97: Solve. See the Concept Checks in this section.Which polynomial(s) i...
 5.3.98: Solve. See the Concept Checks in this section.Which polynomial(s) i...
 5.3.99: Solve. See the Concept Checks in this section. Correct the subtract...
 5.3.100: Solve. See the Concept Checks in this section.Correct the addition....
 5.3.101: Solve. See the Concept Checks in this section.Write a function, P1x...
 5.3.102: Solve. See the Concept Checks in this section.Write a function, R1x...
 5.3.103: Solve. See the Concept Checks in this section.In your own words, de...
 5.3.104: Solve. See the Concept Checks in this section.In your own words, de...
 5.3.105: Perform the indicated operations.14x2a  3xa + 0.52  1x2a  5xa  ...
 5.3.106: Perform the indicated operations.14x2a  3xa + 0.52  1x2a  5xa  ...
 5.3.107: Perform the indicated operations. 18x2y  7xy + 32 + 1 4x2y + 9xy ...
 5.3.108: Perform the indicated operations.114z5x + 3z2x + z2  12z5x  10z2x...
 5.3.109: Find each perimeter(x 5y)units(3x2 x 2y)units
 5.3.110: Find each perimeter(z 2)units(z3 4z 1)units(2z2 z) units
 5.3.111: If P1x2 = 3x + 3, Q1x2 = 4x2  6x + 3, and R1x2 = 5x2  7, find the...
 5.3.112: If P1x2 = 3x + 3, Q1x2 = 4x2  6x + 3, and R1x2 = 5x2  7, find the...
 5.3.113: If P1x2 = 3x + 3, Q1x2 = 4x2  6x + 3, and R1x2 = 5x2  7, find the...
 5.3.114: If P1x2 = 3x + 3, Q1x2 = 4x2  6x + 3, and R1x2 = 5x2  7, find the...
 5.3.115: If P1x2 = 3x + 3, Q1x2 = 4x2  6x + 3, and R1x2 = 5x2  7, find the...
 5.3.116: If P1x2 = 3x + 3, Q1x2 = 4x2  6x + 3, and R1x2 = 5x2  7, find the...
 5.3.117: If P1x2 = 3x + 3, Q1x2 = 4x2  6x + 3, and R1x2 = 5x2  7, find the...
 5.3.118: If P1x2 = 3x + 3, Q1x2 = 4x2  6x + 3, and R1x2 = 5x2  7, find the...
 5.3.119: If P1x2 is the polynomial given, find a. P1a2, b. P1 x2, and c. P1...
 5.3.120: If P1x2 is the polynomial given, find a. P1a2, b. P1 x2, and c. P1...
 5.3.121: If P1x2 is the polynomial given, find a. P1a2, b. P1 x2, and c. P1...
 5.3.122: If P1x2 is the polynomial given, find a. P1a2, b. P1 x2, and c. P1...
 5.3.123: If P1x2 is the polynomial given, find a. P1a2, b. P1 x2, and c. P1...
 5.3.124: If P1x2 is the polynomial given, find a. P1a2, b. P1 x2, and c. P1...
 5.3.125: The function f 1x2 = 0.19x2 + 5.67x + 43.7 can be used toapproximat...
 5.3.126: The function f(x) = 0.0007x2 + 0.24x + 7.98 can be usedto approxima...
Solutions for Chapter 5.3: Polynomials and Polynomial Functions
Full solutions for Intermediate Algebra  6th Edition
ISBN: 9780321785046
Solutions for Chapter 5.3: Polynomials and Polynomial Functions
Get Full SolutionsSince 126 problems in chapter 5.3: Polynomials and Polynomial Functions have been answered, more than 66749 students have viewed full stepbystep solutions from this chapter. Chapter 5.3: Polynomials and Polynomial Functions includes 126 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Intermediate Algebra, edition: 6. Intermediate Algebra was written by and is associated to the ISBN: 9780321785046.

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.

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

Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

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

GramSchmidt orthogonalization A = QR.
Independent columns in A, orthonormal columns in Q. Each column q j of Q is a combination of the first j columns of A (and conversely, so R is upper triangular). Convention: diag(R) > o.

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

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.

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

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

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

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

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

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 ().

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

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.

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.