 R.5 .1: If factored completely 3x3  12x =
 R.5 .2: If a polynomial cannot be written as the product of two other polyn...
 R.5 .3: True or False The polynomial is prime.
 R.5 .4: True or False 3x3  2x2  6x + 4 = 13x  221x2 + 22.
 R.5 .5: In 514, factor each polynomial by removing the common monomial fact...
 R.5 .6: In 514, factor each polynomial by removing the common monomial fact...
 R.5 .7: In 514, factor each polynomial by removing the common monomial fact...
 R.5 .8: In 514, factor each polynomial by removing the common monomial fact...
 R.5 .9: In 514, factor each polynomial by removing the common monomial fact...
 R.5 .10: In 514, factor each polynomial by removing the common monomial fact...
 R.5 .11: In 514, factor each polynomial by removing the common monomial fact...
 R.5 .12: In 514, factor each polynomial by removing the common monomial fact...
 R.5 .13: In 514, factor each polynomial by removing the common monomial fact...
 R.5 .14: In 514, factor each polynomial by removing the common monomial fact...
 R.5 .15: In 1522, factor the difference of two squares. x2  1
 R.5 .16: In 1522, factor the difference of two squares. x2  4
 R.5 .17: In 1522, factor the difference of two squares. 4x2  1
 R.5 .18: In 1522, factor the difference of two squares. 9x2  1
 R.5 .19: In 1522, factor the difference of two squares. x2  16
 R.5 .20: In 1522, factor the difference of two squares. x2  25
 R.5 .21: In 1522, factor the difference of two squares. 25x2  4
 R.5 .22: In 1522, factor the difference of two squares. . 36x2  9
 R.5 .23: In 2332, factor the perfect squares x2 + 2x + 1
 R.5 .24: In 2332, factor the perfect squares x2  4x + 4
 R.5 .25: In 2332, factor the perfect squares x2 + 4x + 4
 R.5 .26: In 2332, factor the perfect squares x2  2x + 1
 R.5 .27: In 2332, factor the perfect squares x2  10x + 25
 R.5 .28: In 2332, factor the perfect squares x2 + 10x + 25
 R.5 .29: In 2332, factor the perfect squares 4x2 + 4x + 1
 R.5 .30: In 2332, factor the perfect squares 9x2 + 6x + 1
 R.5 .31: In 2332, factor the perfect squares 16x2 + 8x + 1
 R.5 .32: In 2332, factor the perfect squares 25x2 + 10x + 1
 R.5 .33: In 3338, factor the sum or difference of two cubes. x3  27
 R.5 .34: In 3338, factor the sum or difference of two cubes. x3 + 125
 R.5 .35: In 3338, factor the sum or difference of two cubes. x3 + 27
 R.5 .36: In 3338, factor the sum or difference of two cubes. 27  8x3
 R.5 .37: In 3338, factor the sum or difference of two cubes. 8x3 + 27
 R.5 .38: In 3338, factor the sum or difference of two cubes. 64  27x3
 R.5 .39: In 3950, factor each polynomial. x2 + 5x + 6
 R.5 .40: In 3950, factor each polynomial. x2 + 6x + 8
 R.5 .41: In 3950, factor each polynomial. x2 + 7x + 6
 R.5 .42: In 3950, factor each polynomial. x2 + 9x + 8
 R.5 .43: In 3950, factor each polynomial. x2 + 7x + 10
 R.5 .44: In 3950, factor each polynomial. x2 + 11x + 10
 R.5 .45: In 3950, factor each polynomial. x2  10x + 16
 R.5 .46: In 3950, factor each polynomial. x2  17x + 16
 R.5 .47: In 3950, factor each polynomial. x2  7x  8
 R.5 .48: In 3950, factor each polynomial. x2  2x  8
 R.5 .49: In 3950, factor each polynomial. x2 + 7x  8
 R.5 .50: In 3950, factor each polynomial. x2 + 2x  8
 R.5 .51: In 5156, factor by grouping. 2x2 + 4x + 3x + 6
 R.5 .52: In 5156, factor by grouping. 3x2  3x + 2x  2
 R.5 .53: In 5156, factor by grouping. 2x2  4x + x  2
 R.5 .54: In 5156, factor by grouping. 3x2 + 6x  x  2
 R.5 .55: In 5156, factor by grouping. 6x2 + 9x + 4x + 6
 R.5 .56: In 5156, factor by grouping. 9x2  6x + 3x  2
 R.5 .57: In 5768, factor each polynomial. 3x2 + 4x + 1
 R.5 .58: In 5768, factor each polynomial. 2x2 + 3x + 1
 R.5 .59: In 5768, factor each polynomial. 2z2 + 5z + 3
 R.5 .60: In 5768, factor each polynomial. 6z2 + 5z + 1
 R.5 .61: In 5768, factor each polynomial. 3x2 + 2x  8
 R.5 .62: In 5768, factor each polynomial. 3x2 + 10x + 8
 R.5 .63: In 5768, factor each polynomial. 3x2  2x  8
 R.5 .64: In 5768, factor each polynomial. 3x2  10x + 8
 R.5 .65: In 5768, factor each polynomial. 3x2 + 14x + 8
 R.5 .66: In 5768, factor each polynomial. 3x2  14x + 8
 R.5 .67: In 5768, factor each polynomial. 3x2 + 10x  8
 R.5 .68: In 5768, factor each polynomial. 3x2  10x  8
 R.5 .69: In 6974, determine the number that should be added to complete the ...
 R.5 .70: In 6974, determine the number that should be added to complete the ...
 R.5 .71: In 6974, determine the number that should be added to complete the ...
 R.5 .72: In 6974, determine the number that should be added to complete the ...
 R.5 .73: In 6974, determine the number that should be added to complete the ...
 R.5 .74: In 6974, determine the number that should be added to complete the ...
 R.5 .75: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .76: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .77: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .78: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .79: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .80: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .81: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .82: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .83: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .84: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .85: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .86: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .87: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .88: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .89: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .90: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .91: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .92: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .93: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .94: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .95: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .96: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .97: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .98: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .99: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .100: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .101: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .102: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .103: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .104: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .105: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .106: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .107: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .108: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .109: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .110: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .111: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .112: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .113: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .114: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .115: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .116: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .117: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .118: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .119: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .120: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .121: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .122: In 75122, factor completely each polynomial. If the polynomial cann...
 R.5 .123: In 123132, expressions that occur in calculus are given. Factor com...
 R.5 .124: In 123132, expressions that occur in calculus are given. Factor com...
 R.5 .125: In 123132, expressions that occur in calculus are given. Factor com...
 R.5 .126: In 123132, expressions that occur in calculus are given. Factor com...
 R.5 .127: In 123132, expressions that occur in calculus are given. Factor com...
 R.5 .128: In 123132, expressions that occur in calculus are given. Factor com...
 R.5 .129: In 123132, expressions that occur in calculus are given. Factor com...
 R.5 .130: In 123132, expressions that occur in calculus are given. Factor com...
 R.5 .131: In 123132, expressions that occur in calculus are given. Factor com...
 R.5 .132: In 123132, expressions that occur in calculus are given. Factor com...
 R.5 .133: Show that is prime. x2 + 4
 R.5 .134: Show that is prime.
 R.5 .135: Make up a polynomial that factors into a perfect square.
 R.5 .136: Explain to a fellow student what you look for first when presented ...
Solutions for Chapter R.5 : Factoring Polynomials
Full solutions for College Algebra  9th Edition
ISBN: 9780321716811
Solutions for Chapter R.5 : Factoring Polynomials
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. College Algebra was written by and is associated to the ISBN: 9780321716811. This textbook survival guide was created for the textbook: College Algebra, edition: 9. Chapter R.5 : Factoring Polynomials includes 136 full stepbystep solutions. Since 136 problems in chapter R.5 : Factoring Polynomials have been answered, more than 53627 students have viewed full stepbystep solutions from this chapter.

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

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

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.

Covariance matrix:E.
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.

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

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).

Hilbert matrix hilb(n).
Entries HU = 1/(i + j 1) = Jd X i 1 xj1dx. Positive definite but extremely small Amin and large condition number: H is illconditioned.

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

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

Linear transformation T.
Each vector V in the input space transforms to T (v) in the output space, and linearity requires T(cv + dw) = c T(v) + d T(w). Examples: Matrix multiplication A v, differentiation and integration in function space.

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.

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

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

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

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

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.