 73.1: State whether each expression is a polynomial. If the expression is...
 73.2: State whether each expression is a polynomial. If the expression is...
 73.3: State whether each expression is a polynomial. If the expression is...
 73.4: GEOMETRY Write a polynomial to represent the area of the shaded reg...
 73.5: Find the degree of each polynomial.
 73.6: Find the degree of each polynomial.
 73.7: Find the degree of each polynomial.
 73.8: Arrange the terms of each polynomial so that the powers of x are in...
 73.9: Arrange the terms of each polynomial so that the powers of x are in...
 73.10: Arrange the terms of each polynomial so that the powers of x are in...
 73.11: Arrange the terms of each polynomial so that the powers of x are in...
 73.12: State whether each expression is a polynomial. If the expression is...
 73.13: State whether each expression is a polynomial. If the expression is...
 73.14: State whether each expression is a polynomial. If the expression is...
 73.15: State whether each expression is a polynomial. If the expression is...
 73.16: State whether each expression is a polynomial. If the expression is...
 73.17: State whether each expression is a polynomial. If the expression is...
 73.18: GEOMETRY Write a polynomial to represent the area of each shaded re...
 73.19: GEOMETRY Write a polynomial to represent the area of each shaded re...
 73.20: GEOMETRY Write a polynomial to represent the area of each shaded re...
 73.21: GEOMETRY Write a polynomial to represent the area of each shaded re...
 73.22: Find the degree of each polynomial.
 73.23: Find the degree of each polynomial.
 73.24: Find the degree of each polynomial.
 73.25: Find the degree of each polynomial.
 73.26: Find the degree of each polynomial.
 73.27: Find the degree of each polynomial.
 73.28: Find the degree of each polynomial.
 73.29: Find the degree of each polynomial.
 73.30: Find the degree of each polynomial.
 73.31: Find the degree of each polynomial.
 73.32: Find the degree of each polynomial.
 73.33: Find the degree of each polynomial.
 73.34: Arrange the terms of each polynomial so that the powers of x are in...
 73.35: Arrange the terms of each polynomial so that the powers of x are in...
 73.36: Arrange the terms of each polynomial so that the powers of x are in...
 73.37: Arrange the terms of each polynomial so that the powers of x are in...
 73.38: Arrange the terms of each polynomial so that the powers of x are in...
 73.39: Arrange the terms of each polynomial so that the powers of x are in...
 73.40: Arrange the terms of each polynomial so that the powers of x are in...
 73.41: Arrange the terms of each polynomial so that the powers of x are in...
 73.42: Arrange the terms of each polynomial so that the powers of x are in...
 73.43: Arrange the terms of each polynomial so that the powers of x are in...
 73.44: Arrange the terms of each polynomial so that the powers of x are in...
 73.45: Arrange the terms of each polynomial so that the powers of x are in...
 73.46: Arrange the terms of each polynomial so that the powers of x are in...
 73.47: Arrange the terms of each polynomial so that the powers of x are in...
 73.48: Arrange the terms of each polynomial so that the powers of x are in...
 73.49: Arrange the terms of each polynomial so that the powers of x are in...
 73.50: MONEY Write a polynomial to represent the value of q quarters, d di...
 73.51: MULTIPLE BIRTHS The rate of quadruplet births Q in the United State...
 73.52: PACKAGING For Exercises 52 and 53, use the following information. A...
 73.53: PACKAGING For Exercises 52 and 53, use the following information. A...
 73.54: Write two polynomials that represent the perimeter and area of the ...
 73.55: OPEN ENDED Give an example of a monomial of degree zero.
 73.56: REASONING Explain why a polynomial cannot contain a variable term w...
 73.57: CHALLENGE Tell whether the following statement is true or false. Ex...
 73.58: REASONING Determine whether each statement is true or false. If fal...
 73.59: Writing in Math Use the information about video game usage on page ...
 73.60: Which expression could be used to represent the area of the shaded ...
 73.61: REVIEW Lawanda rolled a sixsided game cube 30 times and recorded h...
 73.62: Simplify. Assume that no denominator is equal to zero. (
 73.63: Simplify. Assume that no denominator is equal to zero. (
 73.64: Simplify. Assume that no denominator is equal to zero. (
 73.65: Simplify. Assume that no denominator is equal to zero. (
 73.66: Determine whether each expression is a monomial. Write yes or no. (
 73.67: Determine whether each expression is a monomial. Write yes or no. (
 73.68: Determine whether each expression is a monomial. Write yes or no. (
 73.69: Determine whether each relation is a function.
 73.70: Determine whether each relation is a function.
 73.71: MAPS The scale of a road map is 1.5 inches = 100 miles. The distanc...
 73.72: Find each square root. Round to the nearest hundredth if necessary. (
 73.73: Find each square root. Round to the nearest hundredth if necessary. (
 73.74: Find each square root. Round to the nearest hundredth if necessary. (
 73.75: PREREQUISITE SKILL Simplify each expression, if possible. If not po...
 73.76: PREREQUISITE SKILL Simplify each expression, if possible. If not po...
 73.77: PREREQUISITE SKILL Simplify each expression, if possible. If not po...
 73.78: PREREQUISITE SKILL Simplify each expression, if possible. If not po...
Solutions for Chapter 73: Polynomials
Full solutions for Algebra 1, Student Edition (MERRILL ALGEBRA 1)  1st Edition
ISBN: 9780078738227
Solutions for Chapter 73: Polynomials
Get Full SolutionsAlgebra 1, Student Edition (MERRILL ALGEBRA 1) was written by and is associated to the ISBN: 9780078738227. Since 78 problems in chapter 73: Polynomials have been answered, more than 35248 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 73: Polynomials includes 78 full stepbystep solutions. This textbook survival guide was created for the textbook: Algebra 1, Student Edition (MERRILL ALGEBRA 1) , edition: 1.

Basis for V.
Independent vectors VI, ... , v d whose linear combinations give each vector in V as v = CIVI + ... + CdVd. V has many bases, each basis gives unique c's. A vector space has many bases!

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.

Column space C (A) =
space of all combinations of the columns of A.

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).

Cyclic shift
S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).

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.

GramSchmidt orthogonalization A = QR.
Independent columns in A, orthonormal columns in Q. Each column q j of Q is a combination of the first j columns of A (and conversely, so R is upper triangular). Convention: diag(R) > o.

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

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

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

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

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

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

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.

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.