 64.1: 5x6  8x2
 64.2: 2b + 4b3  3b5  7
 64.3: p(x) = x3 + x2  x
 64.4: p(x) = x4  3x3 + 2x2  5x + 1
 64.5: BIOLOGY The intensity of light emitted by a firefly can be determin...
 64.6: p(a3)
 64.7: 5[q(2a)]
 64.8: 3p(a)  q(a + 1)
 64.9: x f
 64.10: O x f
 64.11: x f(
 64.12: 7  x
 64.13: (a + 1)(a2  4)
 64.14: a2 + 2ab + b2
 64.15: c2 + c  _1 c
 64.16: 6x4 + 3x2 + 4x  8
 64.17: 7 + 3x2  5x3 + 6x2  2x
 64.18: p(x) = 2  x
 64.19: p(x) = x2  3x + 8
 64.20: p(x) = 2x3  x2 + 5x  7
 64.21: p(x) = x5  x2
 64.22: r(3a)
 64.23: 4p(a)
 64.24: p(a2)
 64.25: p(2a3)
 64.26: r(x + 1)
 64.27: p(x2 + 3)
 64.28: For each graph, a. describe the end behavior, b. determine whether ...
 64.29: For each graph, a. describe the end behavior, b. determine whether ...
 64.30: For each graph, a. describe the end behavior, b. determine whether ...
 64.31: For each graph, a. describe the end behavior, b. determine whether ...
 64.32: For each graph, a. describe the end behavior, b. determine whether ...
 64.33: For each graph, a. describe the end behavior, b. determine whether ...
 64.34: ENERGY The power generated by a windmill is a function of the speed...
 64.35: PHYSICS For a moving object with mass m in kilograms, the kinetic e...
 64.36: p(x) = x4  7x3 + 8x  6
 64.37: p(x) = 7x2  9x + 10
 64.38: p(x) = _1 2 x4  2x2 + 4
 64.39: p(x) = _1 8 x3  _1 4 x2  _1 2 x + 5
 64.40: 2[p(x + 4)]
 64.41: r(x + 1)  r(x2)
 64.42: 3[p(x2  1)] + 4p(x)
 64.43: Is the graph an odddegree or evendegree function?
 64.44: Discuss the end behavior
 64.45: Do you think attendance at Broadway plays will increase or decrease...
 64.46: The number of regions formed by connecting n points of a circle can...
 64.47: Find the number of regions formed by connecting 5 points of a circl...
 64.48: How many points would you have to connect to form 99 regions?
 64.49: REASONING Explain why a constant polynomial such as f(x) = 4 has de...
 64.50: OPEN ENDED Sketch the graph of an odddegree polynomial function wi...
 64.51: REASONING Determine whether the following statement is always, some...
 64.52: Find the value of a.
 64.53: For what value(s) of x will f(x) = 0?
 64.54: Simplify and rewrite the function as a cubic function.
 64.55: Sketch the graph of the function.
 64.56: Writing in Math Use the information on page 331 to explain where po...
 64.57: ACT/SAT The figure at the right shows the graph of a polynomial fun...
 64.58: REVIEW Which polynomial represents (4x2 + 5x  3)(2x  7)? F 8x3  ...
 64.59: (t3  3t + 2) (t + 2)
 64.60: (y2 + 4y + 3)(y + 1)1
 64.61: x3  3x __2 + 2x  6 x  3
 64.62: 3x4 + x3  8x __2 + 10x  3 3x  2
 64.63: BUSINESS Ms. Schifflet is writing a computer program to find the sa...
 64.64: x2  8x  2 = 0
 64.65: x2 + _1 3 x  _35 36 = 0
 64.66: Write an absolute value inequality for each graph.
 64.67: Write an absolute value inequality for each graph.
 64.68: Write an absolute value inequality for each graph.
 64.69: Write an absolute value inequality for each graph.
 64.70: If 3x = 4y and 4y = 15z, then 3x = 15z.
 64.71: 5y(4a  6b) = 20ay  30by
 64.72: 2 + (3 + x) = (2 + 3) + x
 64.73: y = x2 + 4
 64.74: y = x2 + 6x  5
 64.75: y = _1 2 x2 + 2x  6
Solutions for Chapter 64: Polynomial Functions
Full solutions for Algebra 2, Student Edition (MERRILL ALGEBRA 2)  1st Edition
ISBN: 9780078738302
Solutions for Chapter 64: Polynomial Functions
Get Full SolutionsSince 75 problems in chapter 64: Polynomial Functions have been answered, more than 56390 students have viewed full stepbystep solutions from this chapter. Chapter 64: Polynomial Functions includes 75 full stepbystep solutions. Algebra 2, Student Edition (MERRILL ALGEBRA 2) was written by and is associated to the ISBN: 9780078738302. This textbook survival guide was created for the textbook: Algebra 2, Student Edition (MERRILL ALGEBRA 2), edition: 1. This expansive textbook survival guide covers the following chapters and their solutions.

Complete solution x = x p + Xn to Ax = b.
(Particular x p) + (x n in nullspace).

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

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.

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].

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

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

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

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

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

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

Linear transformation T.
Each vector V in the input space transforms to T (v) in the output space, and linearity requires T(cv + dw) = c T(v) + d T(w). Examples: Matrix multiplication A v, differentiation and integration in function space.

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

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

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

Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.

Positive definite matrix A.
Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(D» O.

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

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.

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

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.