 3.2.1: Fill in the blanks. The graphs of all polynomial functions are ____...
 3.2.2: Fill in the blanks. The ________ ________ ________ is used to deter...
 3.2.3: Fill in the blanks. Polynomial functions of the form ________ are o...
 3.2.4: Fill in the blanks. A polynomial function of degree has at most ___...
 3.2.5: Fill in the blanks. If is a zero of a polynomial function then the ...
 3.2.6: Fill in the blanks. If a real zero of a polynomial function is of e...
 3.2.7: Fill in the blanks. A polynomial function is written in ________ fo...
 3.2.8: Fill in the blanks. The ________ ________ Theorem states that if is...
 3.2.9: In Exercises 916, match the polynomial function with its graph. [Th...
 3.2.10: In Exercises 916, match the polynomial function with its graph. [Th...
 3.2.11: In Exercises 916, match the polynomial function with its graph. [Th...
 3.2.12: In Exercises 916, match the polynomial function with its graph. [Th...
 3.2.13: In Exercises 916, match the polynomial function with its graph. [Th...
 3.2.14: In Exercises 916, match the polynomial function with its graph. [Th...
 3.2.15: In Exercises 916, match the polynomial function with its graph. [Th...
 3.2.16: In Exercises 916, match the polynomial function with its graph. [Th...
 3.2.17: In Exercises 1720, sketch the graph of and each transformation.
 3.2.18: In Exercises 1720, sketch the graph of and each transformation.
 3.2.19: In Exercises 1720, sketch the graph of and each transformation.
 3.2.20: In Exercises 1720, sketch the graph of and each transformation.
 3.2.21: In Exercises 2130, describe the righthand and lefthand behavior o...
 3.2.22: In Exercises 2130, describe the righthand and lefthand behavior o...
 3.2.23: In Exercises 2130, describe the righthand and lefthand behavior o...
 3.2.24: In Exercises 2130, describe the righthand and lefthand behavior o...
 3.2.25: In Exercises 2130, describe the righthand and lefthand behavior o...
 3.2.26: In Exercises 2130, describe the righthand and lefthand behavior o...
 3.2.27: In Exercises 2130, describe the righthand and lefthand behavior o...
 3.2.28: In Exercises 2130, describe the righthand and lefthand behavior o...
 3.2.29: In Exercises 2130, describe the righthand and lefthand behavior o...
 3.2.30: In Exercises 2130, describe the righthand and lefthand behavior o...
 3.2.31: GRAPHICAL ANALYSIS In Exercises 3134, use a graphing utility to gra...
 3.2.32: GRAPHICAL ANALYSIS In Exercises 3134, use a graphing utility to gra...
 3.2.33: GRAPHICAL ANALYSIS In Exercises 3134, use a graphing utility to gra...
 3.2.34: GRAPHICAL ANALYSIS In Exercises 3134, use a graphing utility to gra...
 3.2.35: In Exercises 3550, (a) find all the real zeros of the polynomial fu...
 3.2.36: In Exercises 3550, (a) find all the real zeros of the polynomial fu...
 3.2.37: In Exercises 3550, (a) find all the real zeros of the polynomial fu...
 3.2.38: In Exercises 3550, (a) find all the real zeros of the polynomial fu...
 3.2.39: In Exercises 3550, (a) find all the real zeros of the polynomial fu...
 3.2.40: In Exercises 3550, (a) find all the real zeros of the polynomial fu...
 3.2.41: In Exercises 3550, (a) find all the real zeros of the polynomial fu...
 3.2.42: In Exercises 3550, (a) find all the real zeros of the polynomial fu...
 3.2.43: In Exercises 3550, (a) find all the real zeros of the polynomial fu...
 3.2.44: In Exercises 3550, (a) find all the real zeros of the polynomial fu...
 3.2.45: In Exercises 3550, (a) find all the real zeros of the polynomial fu...
 3.2.46: In Exercises 3550, (a) find all the real zeros of the polynomial fu...
 3.2.47: In Exercises 3550, (a) find all the real zeros of the polynomial fu...
 3.2.48: In Exercises 3550, (a) find all the real zeros of the polynomial fu...
 3.2.49: In Exercises 3550, (a) find all the real zeros of the polynomial fu...
 3.2.50: In Exercises 3550, (a) find all the real zeros of the polynomial fu...
 3.2.51: GRAPHICAL ANALYSIS In Exercises 5154, (a) use a graphing utility to...
 3.2.52: GRAPHICAL ANALYSIS In Exercises 5154, (a) use a graphing utility to...
 3.2.53: GRAPHICAL ANALYSIS In Exercises 5154, (a) use a graphing utility to...
 3.2.54: GRAPHICAL ANALYSIS In Exercises 5154, (a) use a graphing utility to...
 3.2.55: In Exercises 55 64, find a polynomial function that has the given z...
 3.2.56: In Exercises 55 64, find a polynomial function that has the given z...
 3.2.57: In Exercises 55 64, find a polynomial function that has the given z...
 3.2.58: In Exercises 55 64, find a polynomial function that has the given z...
 3.2.59: In Exercises 55 64, find a polynomial function that has the given z...
 3.2.60: In Exercises 55 64, find a polynomial function that has the given z...
 3.2.61: In Exercises 55 64, find a polynomial function that has the given z...
 3.2.62: In Exercises 55 64, find a polynomial function that has the given z...
 3.2.63: In Exercises 55 64, find a polynomial function that has the given z...
 3.2.64: In Exercises 55 64, find a polynomial function that has the given z...
 3.2.65: In Exercises 6574, find a polynomial of degree that has the given z...
 3.2.66: In Exercises 6574, find a polynomial of degree that has the given z...
 3.2.67: In Exercises 6574, find a polynomial of degree that has the given z...
 3.2.68: In Exercises 6574, find a polynomial of degree that has the given z...
 3.2.69: In Exercises 6574, find a polynomial of degree that has the given z...
 3.2.70: In Exercises 6574, find a polynomial of degree that has the given z...
 3.2.71: In Exercises 6574, find a polynomial of degree that has the given z...
 3.2.72: In Exercises 6574, find a polynomial of degree that has the given z...
 3.2.73: In Exercises 6574, find a polynomial of degree that has the given z...
 3.2.74: In Exercises 6574, find a polynomial of degree that has the given z...
 3.2.75: In Exercises 7588, sketch the graph of the function by (a) applying...
 3.2.76: In Exercises 7588, sketch the graph of the function by (a) applying...
 3.2.77: In Exercises 7588, sketch the graph of the function by (a) applying...
 3.2.78: In Exercises 7588, sketch the graph of the function by (a) applying...
 3.2.79: In Exercises 7588, sketch the graph of the function by (a) applying...
 3.2.80: In Exercises 7588, sketch the graph of the function by (a) applying...
 3.2.81: In Exercises 7588, sketch the graph of the function by (a) applying...
 3.2.82: In Exercises 7588, sketch the graph of the function by (a) applying...
 3.2.83: In Exercises 7588, sketch the graph of the function by (a) applying...
 3.2.84: In Exercises 7588, sketch the graph of the function by (a) applying...
 3.2.85: In Exercises 7588, sketch the graph of the function by (a) applying...
 3.2.86: In Exercises 7588, sketch the graph of the function by (a) applying...
 3.2.87: In Exercises 7588, sketch the graph of the function by (a) applying...
 3.2.88: In Exercises 7588, sketch the graph of the function by (a) applying...
 3.2.89: In Exercises 8992, use a graphing utility to graph the function. Us...
 3.2.90: In Exercises 8992, use a graphing utility to graph the function. Us...
 3.2.91: In Exercises 8992, use a graphing utility to graph the function. Us...
 3.2.92: In Exercises 8992, use a graphing utility to graph the function. Us...
 3.2.93: In Exercises 9396, use the Intermediate Value Theorem and the table...
 3.2.94: In Exercises 9396, use the Intermediate Value Theorem and the table...
 3.2.95: In Exercises 9396, use the Intermediate Value Theorem and the table...
 3.2.96: In Exercises 9396, use the Intermediate Value Theorem and the table...
 3.2.97: NUMERICAL AND GRAPHICAL ANALYSIS An open box is to be made from a s...
 3.2.98: MAXIMUM VOLUME An open box with locking tabs is to be made from a s...
 3.2.99: CONSTRUCTION A roofing contractor is fabricating gutters from 12in...
 3.2.100: CONSTRUCTION An industrial propane tank is formed by adjoining two ...
 3.2.101: REVENUE The total revenues (in millions of dollars) for Krispy Krem...
 3.2.102: REVENUE The total revenues (in millions of dollars) for Papa Johns ...
 3.2.103: TREE GROWTH The growth of a red oak tree is approximated by the fun...
 3.2.104: REVENUE The total revenue (in millions of dollars) for a company is...
 3.2.105: A fifthdegree polynomial can have five turning points in its graph.
 3.2.106: It is possible for a sixthdegree polynomial to have only one solut...
 3.2.107: The graph of the function given by rises to the left and falls to t...
 3.2.108: CAPSTONE For each graph, describe a polynomial function that could ...
 3.2.109: GRAPHICAL REASONING Sketch a graph of the function given by Explain...
 3.2.110: THINK ABOUT IT For each function, identify the degree of the functi...
 3.2.111: THINK ABOUT IT Sketch the graph of each polynomial function. Then c...
 3.2.112: Explore the transformations of the form (a) Use a graphing utility ...
Solutions for Chapter 3.2: POLYNOMIAL FUNCTIONS OF HIGHER DEGREE
Full solutions for College Algebra  8th Edition
ISBN: 9781439048696
Solutions for Chapter 3.2: POLYNOMIAL FUNCTIONS OF HIGHER DEGREE
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 112 problems in chapter 3.2: POLYNOMIAL FUNCTIONS OF HIGHER DEGREE have been answered, more than 30195 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: College Algebra , edition: 8. College Algebra was written by and is associated to the ISBN: 9781439048696. Chapter 3.2: POLYNOMIAL FUNCTIONS OF HIGHER DEGREE includes 112 full stepbystep solutions.

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

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

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

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

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

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

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

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.

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

Outer product uv T
= column times row = rank one matrix.

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).

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

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

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

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

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

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·