 74.1: Find each sum or difference.
 74.2: Find each sum or difference.
 74.3: Find each sum or difference.
 74.4: Find each sum or difference.
 74.5: Find each sum or difference.
 74.6: Find each sum or difference.
 74.7: Find each sum or difference.
 74.8: Find each sum or difference.
 74.9: POPULATION For Exercises 9 and 10, use the following information. F...
 74.10: POPULATION For Exercises 9 and 10, use the following information. F...
 74.11: Find each sum or difference.
 74.12: Find each sum or difference.
 74.13: Find each sum or difference.
 74.14: Find each sum or difference.
 74.15: Find each sum or difference.
 74.16: Find each sum or difference.
 74.17: Find each sum or difference.
 74.18: Find each sum or difference.
 74.19: Find each sum or difference.
 74.20: Find each sum or difference.
 74.21: Find each sum or difference.
 74.22: Find each sum or difference.
 74.23: GEOMETRY The measures of two sides of a triangle are given. If P is...
 74.24: GEOMETRY The measures of two sides of a triangle are given. If P is...
 74.25: Find each sum or difference.
 74.26: Find each sum or difference.
 74.27: Find each sum or difference.
 74.28: Find each sum or difference.
 74.29: MOVIES For Exercises 29 and 30, use the following information. From...
 74.30: MOVIES For Exercises 29 and 30, use the following information. From...
 74.31: POSTAL SERVICE For Exercises 3133, use the following information. T...
 74.32: POSTAL SERVICE For Exercises 3133, use the following information. T...
 74.33: POSTAL SERVICE For Exercises 3133, use the following information. T...
 74.34: REASONING Explain why 5x y 2 and 3 x 2 y are not like terms.
 74.35: OPEN ENDED Write two polynomials with a difference of 2 x 2 + x + 3.
 74.36: FIND THE ERROR Esteban and Kendra are finding (5a  6b)  (2a + 5b)...
 74.37: CHALLENGE For Exercises 3739, suppose x is an integer.
 74.38: CHALLENGE For Exercises 3739, suppose x is an integer.
 74.39: CHALLENGE For Exercises 3739, suppose x is an integer.
 74.40: Writing in Math Use the information about music sales on page 384 t...
 74.41: The perimeter of the rectangle shown below is 16a + 2b. Which expre...
 74.42: REVIEW The scale factor of two similar polygons is 4:5. The perimet...
 74.43: Find the degree of each polynomial.
 74.44: Find the degree of each polynomial.
 74.45: Find the degree of each polynomial.
 74.46: Find the degree of each polynomial.
 74.47: Simplify. Assume no denominator is equal to zero.
 74.48: Simplify. Assume no denominator is equal to zero.
 74.49: Simplify. Assume no denominator is equal to zero.
 74.50: KEYBOARDING For Exercises 5053, use the table that shows keyboardin...
 74.51: KEYBOARDING For Exercises 5053, use the table that shows keyboardin...
 74.52: KEYBOARDING For Exercises 5053, use the table that shows keyboardin...
 74.53: KEYBOARDING For Exercises 5053, use the table that shows keyboardin...
 74.54: PREREQUISITE SKILL. Simplify.
 74.55: PREREQUISITE SKILL. Simplify.
 74.56: PREREQUISITE SKILL. Simplify.
 74.57: PREREQUISITE SKILL. Simplify.
 74.58: PREREQUISITE SKILL. Simplify.
 74.59: PREREQUISITE SKILL. Simplify.
Solutions for Chapter 74: Adding and Subtracting Polynomials
Full solutions for Algebra 1, Student Edition (MERRILL ALGEBRA 1)  1st Edition
ISBN: 9780078738227
Solutions for Chapter 74: Adding and Subtracting Polynomials
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Algebra 1, Student Edition (MERRILL ALGEBRA 1) , edition: 1. Algebra 1, Student Edition (MERRILL ALGEBRA 1) was written by and is associated to the ISBN: 9780078738227. Since 59 problems in chapter 74: Adding and Subtracting Polynomials have been answered, more than 35308 students have viewed full stepbystep solutions from this chapter. Chapter 74: Adding and Subtracting Polynomials includes 59 full stepbystep solutions.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

Augmented matrix [A b].
Ax = b is solvable when b is in the column space of A; then [A b] has the same rank as A. Elimination on [A b] keeps equations correct.

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

Full row rank r = m.
Independent rows, at least one solution to Ax = b, column space is all of Rm. Full rank means full column rank or full row rank.

Iterative method.
A sequence of steps intended to approach the desired solution.

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.

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.

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

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

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

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.

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

Reflection matrix (Householder) Q = I 2uuT.
Unit vector u is reflected to Qu = u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q1 = Q.

Row picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.

Semidefinite matrix A.
(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

Simplex method for linear programming.
The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!

Singular Value Decomposition
(SVD) A = U:E VT = (orthogonal) ( diag)( orthogonal) First r columns of U and V are orthonormal bases of C (A) and C (AT), AVi = O'iUi with singular value O'i > O. Last columns are orthonormal bases of nullspaces.

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