 69.1: p(x) = x4  10
 69.2: d(x) = 6x3 + 6x2  15x  2
 69.3: p(x) = x3  5x2  22x + 56
 69.4: f(x) = x3  x2  34x  56
 69.5: t(x) = x4  13x2 + 36
 69.6: f(x) = 2x3  7x2  8x + 28
 69.7: GEOMETRY The volume of the rectangular solid is 1430 cubic centimet...
 69.8: f(x) = 6x3 + 5x2  9x + 2
 69.9: f(x) = x4  x3  x2  x  2
 69.10: f(x) = x3 + 6x + 2
 69.11: h(x) = x3 + 8x + 6
 69.12: f(x) = 3x4 + 15
 69.13: n(x) = x5 + 6x3  12x + 18
 69.14: p(x) = 3x3  5x2  11x + 3
 69.15: h(x) = 9x6  5x3 + 27
 69.16: f(x) = x3 + x2  80x  300
 69.17: p(x) = x3  3x  2
 69.18: f(x) = 2x5  x4  2x + 1
 69.19: f(x) = x5  6x3 + 8x
 69.20: g(x) = x4  3x3 + x2  3x
 69.21: p(x) = x4 + 10x3 + 33x2 + 38x + 8
 69.22: p(x) = 6x4 + 22x3 + 11x2  38x  40
 69.23: g(x) = 5x4  29x3 + 55x2  28x
 69.24: h(x) = 6x3 + 11x2  3x  2
 69.25: p(x) = x3 + 3x2  25x + 21
 69.26: h(x) = 10x3  17x2  7x + 2
 69.27: g(x) = 48x4  52x3 + 13x  3
 69.28: p(x) = x5  2x4  12x3  12x2  13x  10
 69.29: h(x) = 9x5  94x3 + 27x2 + 40x  12
 69.30: Use a rectangular prism to model the cargo space. Write a polynomia...
 69.31: Will a package 34 inches long, 44 inches wide, and 34 inches tall f...
 69.32: Write a polynomial equation that represents the volume of a can. Us...
 69.33: What are the possible values of r? Which values are reasonable here?
 69.34: Find the dimensions of the can
 69.35: If the height of the scale model is 9 inches less than its length, ...
 69.36: If the volume is 6300 cubic inches, write an equation for the situa...
 69.37: What are the dimensions of the scale model?
 69.38: Find all of the zeros of f(x) = x3  2x2 + 3 and g(x) = 2x3  7x2 +...
 69.39: Determine which function, f or g, is shown in the graph at the right.
 69.40: FIND THE ERROR Lauren and Luis are listing the possible rational ze...
 69.41: OPEN ENDED Write a polynomial function that has possible rational z...
 69.42: CHALLENGE If k and 2k are zeros of f(x) = x3 + 4x2 + 9kx  90, find...
 69.43: Writing in Math Use the information on page 369 to explain how the ...
 69.44: Which of the following is a zero of the function f(x) = 12x5  5x3 ...
 69.45: REVIEW A window is in the shape of an equilateral triangle. Each si...
 69.46: g(x) = x3 + 4x2  27x  90; 3
 69.47: h(x) = x3  11x + 20; 2 + i
 69.48: f(x) = x3 + 5x2 + 9x + 45; 5
 69.49: g(x) = x3  3x2  41x + 203; 7
 69.50: 20x3  29x2  25x + 6; x  2
 69.51: 3x4  21x3 + 38x2  14x + 24; x  3
 69.52: GEOMETRY The perimeter of a right triangle is 24 centimeters. Three...
Solutions for Chapter 69: Rational Zero Theorem
Full solutions for Algebra 2, Student Edition (MERRILL ALGEBRA 2)  1st Edition
ISBN: 9780078738302
Solutions for Chapter 69: Rational Zero Theorem
Get Full SolutionsSince 52 problems in chapter 69: Rational Zero Theorem have been answered, more than 53530 students have viewed full stepbystep solutions from this chapter. Chapter 69: Rational Zero Theorem includes 52 full stepbystep solutions. This textbook survival guide was created for the textbook: Algebra 2, Student Edition (MERRILL ALGEBRA 2), edition: 1. Algebra 2, Student Edition (MERRILL ALGEBRA 2) was written by and is associated to the ISBN: 9780078738302. This expansive textbook survival guide covers the following chapters and their solutions.

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

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.

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

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

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

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.

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

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

Lucas numbers
Ln = 2,J, 3, 4, ... satisfy Ln = L n l +Ln 2 = A1 +A~, with AI, A2 = (1 ± /5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.

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

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

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

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.