 6.3.1: Simplify.
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 6.3.3: The number of cookies produced in a factory each day can be estimat...
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 6.3.10: Which expression is equal to (x2  4x + 6)(x  3)1? A x  1 B x  ...
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 6.3.35: A magician gives these instructions to a volunteer. Choose a number...
 6.3.36: Perform the division indicated by 3500a _2 a2 + 100
 6.3.37: About how many subscriptions will be sold if $1500 is spent on adve...
 6.3.38: Find the distance the object travels between the times t = 2 and t ...
 6.3.39: How much time elapses between t = 2 and t = x?
 6.3.40: Find a simplified expression for the average speed of the object be...
 6.3.41: Write a quotient of two polynomials such that the remainder is 5
 6.3.42: Review any of the division problems in this lesson. What is the rel...
 6.3.43: Shelly and Jorge are dividing x3  2x2 + x  3 by x  4. Who is cor...
 6.3.44: Suppose the result of dividing one polynomial by another is r2  6r...
 6.3.45: Use the information on page 325 to explain how you can use division...
 6.3.46: What is the remainder when x3 7x + 5 is divided by x + 3? A 11 C 1...
 6.3.47: If i =  1 , then 5i(7i) = F 70 H 35 G 35 J 70
 6.3.48: Simplify.
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 6.3.52: Earth is an average of 1.5 1011 meters from the Sun. Light travels ...
 6.3.53: Given f(x) = x2  5x + 6, find each value
 6.3.54: Given f(x) = x2  5x + 6, find each value
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 6.3.56: Given f(x) = x2  5x + 6, find each value
Solutions for Chapter 6.3: Dividing Polynomials
Full solutions for California Algebra 2: Concepts, Skills, and Problem Solving  1st Edition
ISBN: 9780078778568
Solutions for Chapter 6.3: Dividing Polynomials
Get Full SolutionsCalifornia Algebra 2: Concepts, Skills, and Problem Solving was written by and is associated to the ISBN: 9780078778568. Chapter 6.3: Dividing Polynomials includes 56 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 56 problems in chapter 6.3: Dividing Polynomials have been answered, more than 47360 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: California Algebra 2: Concepts, Skills, and Problem Solving, edition: 1.

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.

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

Diagonalizable matrix A.
Must have n independent eigenvectors (in the columns of S; automatic with n different eigenvalues). Then SI AS = A = eigenvalue 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.

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

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

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)·(b  Ax) = o.

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.

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

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

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

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.

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