- 6.3.1: Simplify.
- 6.3.2: Simplify.
- 6.3.3: The number of cookies produced in a factory each day can be estimat...
- 6.3.4: Simplify.
- 6.3.5: Simplify.
- 6.3.6: Simplify.
- 6.3.7: Simplify.
- 6.3.8: Simplify.
- 6.3.9: Simplify.
- 6.3.10: Which expression is equal to (x2 - 4x + 6)(x - 3)-1? A x - 1 B x - ...
- 6.3.11: Simplify
- 6.3.12: Simplify
- 6.3.13: Simplify
- 6.3.14: Simplify
- 6.3.15: Simplify
- 6.3.16: Simplify
- 6.3.17: Simplify
- 6.3.18: Simplify
- 6.3.19: Simplify
- 6.3.20: Simplify
- 6.3.21: Simplify
- 6.3.22: Simplify
- 6.3.23: Simplify
- 6.3.24: Simplify
- 6.3.25: Simplify
- 6.3.26: Simplify
- 6.3.27: Simplify
- 6.3.28: Simplify
- 6.3.29: Simplify
- 6.3.30: Simplify
- 6.3.31: Simplify
- 6.3.32: Simplify
- 6.3.33: Simplify
- 6.3.34: Simplify
- 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.
- 6.3.49: Simplify.
- 6.3.50: Simplify.
- 6.3.51: Simplify.
- 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
- 6.3.55: Given f(x) = x2 - 5x + 6, find each value
- 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
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).
Tv = Av + Vo = linear transformation plus shift.
Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.
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 n-l - An).
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 S-I 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.
= Xl (column 1) + ... + xn(column n) = combination of columns.
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.
Every v in V is orthogonal to every w in W.
Outer product uv T
= column times row = rank one matrix.
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 = U-I.
Orthonormal columns (complex analog of Q).