 6.9.1: List all of the possible rational zeros of each function.
 6.9.2: List all of the possible rational zeros of each function.
 6.9.3: Find all of the rational zeros of each function
 6.9.4: Find all of the rational zeros of each function
 6.9.5: Find all of the rational zeros of each function
 6.9.6: Find all of the rational zeros of each function
 6.9.7: The volume of the rectangular solid is 1430 cubic centimeters. Find...
 6.9.8: Find all of the zeros of each function.
 6.9.9: Find all of the zeros of each function.
 6.9.10: List all of the possible rational zeros of each function
 6.9.11: List all of the possible rational zeros of each function
 6.9.12: List all of the possible rational zeros of each function
 6.9.13: List all of the possible rational zeros of each function
 6.9.14: List all of the possible rational zeros of each function
 6.9.15: List all of the possible rational zeros of each function
 6.9.16: Find all of the rational zeros of each function
 6.9.17: Find all of the rational zeros of each function
 6.9.18: Find all of the rational zeros of each function
 6.9.19: Find all of the rational zeros of each function
 6.9.20: Find all of the rational zeros of each function
 6.9.21: Find all of the rational zeros of each function
 6.9.22: Find all of the zeros of each function.
 6.9.23: Find all of the zeros of each function.
 6.9.24: Find all of the zeros of each function.
 6.9.25: Find all of the zeros of each function.
 6.9.26: Find all of the zeros of each function.
 6.9.27: Find all of the zeros of each function.
 6.9.28: Find all of the zeros of each function.
 6.9.29: Find all of the zeros of each function.
 6.9.30: Use a rectangular prism to model the cargo space. Write a polynomia...
 6.9.31: Will a package 34 inches long, 44 inches wide, and 34 inches tall f...
 6.9.32: Write a polynomial equation that represents the volume of a can. Us...
 6.9.33: What are the possible values of r? Which values are reasonable here?
 6.9.34: Find the dimensions of the can.
 6.9.35: If the height of the scale model is 9 inches less than its length, ...
 6.9.36: If the volume is 6300 cubic inches, write an equation for the situa...
 6.9.37: What are the dimensions of the scale model?
 6.9.38: Find all of the zeros of f(x) = x3  2x2 + 3 and g(x) = 2x3  7x2 +...
 6.9.39: Determine which function, f or g, is shown in the graph at the right
 6.9.40: Lauren and Luis are listing the possible rational zeros of f(x) = 4...
 6.9.41: Write a polynomial function that has possible rational zeros of 1, ...
 6.9.42: If k and 2k are zeros of f(x) = x3 + 4x2 + 9kx  90, find k and all...
 6.9.43: Use the information on page 369 to explain how the Rational Zero Th...
 6.9.44: Which of the following is a zero of the function f(x) = 12x5  5x3 ...
 6.9.45: A window is in the shape of an equilateral triangle. Each side of t...
 6.9.46: Given a function and one of its zeros, find all of the zeros of the...
 6.9.47: Given a function and one of its zeros, find all of the zeros of the...
 6.9.48: Given a function and one of its zeros, find all of the zeros of the...
 6.9.49: Given a function and one of its zeros, find all of the zeros of the...
 6.9.50: Given a polynomial and one of its factors, find the remaining facto...
 6.9.51: Given a polynomial and one of its factors, find the remaining facto...
 6.9.52: The perimeter of a right triangle is 24 centimeters. Three times th...
Solutions for Chapter 6.9: Rational Zero Theorem
Full solutions for California Algebra 2: Concepts, Skills, and Problem Solving  1st Edition
ISBN: 9780078778568
Solutions for Chapter 6.9: Rational Zero Theorem
Get Full SolutionsSince 52 problems in chapter 6.9: Rational Zero Theorem have been answered, more than 42858 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. California Algebra 2: Concepts, Skills, and Problem Solving was written by and is associated to the ISBN: 9780078778568. Chapter 6.9: Rational Zero Theorem includes 52 full stepbystep solutions. This textbook survival guide was created for the textbook: California Algebra 2: Concepts, Skills, and Problem Solving, edition: 1.

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

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

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.

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

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.

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

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

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.

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.

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

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

Orthonormal vectors q 1 , ... , q n·
Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q 1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

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

Positive definite matrix A.
Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(D» O.

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

Rotation matrix
R = [~ CS ] rotates the plane by () and R 1 = RT rotates back by (). Eigenvalues are eiO and eiO , eigenvectors are (1, ±i). c, s = cos (), sin ().

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!

Sum V + W of subs paces.
Space of all (v in V) + (w in W). Direct sum: V n W = to}.