 P.4.1: In Exercises 14 is ilre algebraic expression a polynomial? If it i...
 P.4.2: In Exercises 14 is ilre algebraic expression a polynomial? If it i...
 P.4.3: In Exercises 14 is ilre algebraic expression a polynomial? If it i...
 P.4.4: In Exercises 14 is ilre algebraic expression a polynomial? If it i...
 P.4.5: In Exercises 58, find the degree of the polynomial. 3x2  5x + 4
 P.4.6: In Exercises 58, find the degree of the polynomial.  4x3 + 7x2  11
 P.4.7: In Exercises 58, find the degree of the polynomial. x'  4.t3 + 9x...
 P.4.8: In Exercises 58, find the degree of the polynomial. x 2  &J + 15x...
 P.4.9: In Exercises 914.perform the indicated operadons. Writ.e the resul...
 P.4.10: In Exercises 914.perform the indicated operadons. Writ.e the resul...
 P.4.11: In Exercises 914.perform the indicated operadons. Writ.e the resul...
 P.4.12: In Exercises 914.perform the indicated operadons. Writ.e the resul...
 P.4.13: In Exercises 914.perform the indicated operadons. Writ.e the resul...
 P.4.14: In Exercises 914.perform the indicated operadons. Writ.e the resul...
 P.4.15: In Exercises 1558,find each product. (.t + 1)(.t2  x + l)
 P.4.16: In Exercises 1558,find each product. .t + 5}(.t2  5x + 25)
 P.4.17: In Exercises 1558,find each product. (2t  3)(x'  3x + 5)
 P.4.18: In Exercises 1558,find each product. (2t  l)(x'  4x + 3)
 P.4.19: In Exercises 1558,find each product. (.t + 7)(x + 3)
 P.4.20: In Exercises 1558,find each product. .t + 8)(x + 5)
 P.4.21: In Exercises 1558,find each product. (x  5)(x + 3)
 P.4.22: In Exercises 1558,find each product. x  1)(x + 2)
 P.4.23: In Exercises 1558,find each product. (3.t + 5)(2t + 1)
 P.4.24: In Exercises 1558,find each product. 7.t + 4)(3x + 1)
 P.4.25: In Exercises 1558,find each product. (2t  3)(5x + 3)
 P.4.26: In Exercises 1558,find each product. (2t  5)(7x + 2)
 P.4.27: In Exercises 1558,find each product. (5x2  4)(3x2  7)
 P.4.28: In Exercises 1558,find each product. (7x2  2)(3x2  5)
 P.4.29: In Exercises 1558,find each product. &t3 + 3)(x2  5)
 P.4.30: In Exercises 1558,find each product. (7x3 + 5)(x2  2)
 P.4.31: In Exercises 1558,find each product. (.t + 3)(.t  3)
 P.4.32: In Exercises 1558,find each product. (.t + 5)(x  5)
 P.4.33: In Exercises 1558,find each product. (3x + 2)(3x  2)
 P.4.34: In Exercises 1558,find each product. (2t + 5)(2t  5)
 P.4.35: In Exercises 1558,find each product. (5  7x)(5 + 1x)
 P.4.36: In Exercises 1558,find each product. (4  3x)(4 + 3x)
 P.4.37: In Exercises 1558,find each product. (4x2 + 5x)(4x1  5.t)
 P.4.38: In Exercises 1558,find each product. (3x2 + 4x)(3x1  4t)
 P.4.39: In Exercises 1558,find each product. (1  y')(l + y5)
 P.4.40: In Exercises 1558,find each product. 2  y')(2 + y5)
 P.4.41: In Exercises 1558,find each product. (x + 2)'
 P.4.42: In Exercises 1558,find each product. (x + 5)'
 P.4.43: In Exercises 1558,find each product. (2t + 3)'
 P.4.44: In Exercises 1558,find each product. (3.t + 2)2
 P.4.45: In Exercises 1558,find each product. (x  3)'
 P.4.46: In Exercises 1558,find each product. (x  4)'
 P.4.47: In Exercises 1558,find each product. (4x2  t)'
 P.4.48: In Exercises 1558,find each product. (5x2  3)'
 P.4.49: In Exercises 1558,find each product. (7  2r)2
 P.4.50: In Exercises 1558,find each product. (9  5x)2
 P.4.51: In Exercises 1558,find each product. (.t + 1)3
 P.4.52: In Exercises 1558,find each product. (.t + 2)3
 P.4.53: In Exercises 1558,find each product. (2t + 3)3
 P.4.54: In Exercises 1558,find each product. (3x + 4)3
 P.4.55: In Exercises 1558,find each product. (.t  3)'
 P.4.56: In Exercises 1558,find each product. (.t  1)'
 P.4.57: In Exercises 1558,find each product. (3x  4)3
 P.4.58: In Exercises 1558,find each product. (2t  3)3
 P.4.59: In Exercises 5966. perfomr 1he indicated operations .. Indicate th...
 P.4.60: In Exercises 5966. perfomr 1he indicated operations .. Indicate th...
 P.4.61: In Exercises 5966. perfomr 1he indicated operations .. Indicate th...
 P.4.62: In Exercises 5966. perfomr 1he indicated operations .. Indicate th...
 P.4.63: In Exercises 5966. perfomr 1he indicated operations .. Indicate th...
 P.4.64: In Exercises 5966. perfomr 1he indicated operations .. Indicate th...
 P.4.65: In Exercises 5966. perfomr 1he indicated operations .. Indicate th...
 P.4.66: In Exercises 5966. perfomr 1he indicated operations .. Indicate th...
 P.4.67: In Exercises 6782.find each product. ~+~0+~
 P.4.68: In Exercises 6782.find each product. ~+~~+~
 P.4.69: In Exercises 6782.find each product. (x  3y)(2t + 7y)
 P.4.70: In Exercises 6782.find each product. (3x  y)(2t + 5y)
 P.4.71: In Exercises 6782.find each product. (3xy  1 )(5xy + 2)
 P.4.72: In Exercises 6782.find each product. (7x2y + 1)(2x2y  3)
 P.4.73: In Exercises 6782.find each product. 7x + 5y)2
 P.4.74: In Exercises 6782.find each product. (9x + 7y)2
 P.4.75: In Exercises 6782.find each product. (r2y'  3)2
 P.4.76: In Exercises 6782.find each product. (r2y'  5)2
 P.4.77: In Exercises 6782.find each product. (x  y)(x1 + xy + y')
 P.4.78: In Exercises 6782.find each product. (x + y)(x1  xy + y')
 P.4.79: In Exercises 6782.find each product. (3x + 5y)(3.t  5y)
 P.4.80: In Exercises 6782.find each product. (7x + 3y)(7x  3y)
 P.4.81: In Exercises 6782.find each product. (7xy 2  t0y)(7xy2 + lOy)
 P.4.82: In Exercises 6782.find each product. (3xy 2  4y)(3xy2 + 4y)
 P.4.83: In Exercises 8390, perform fire indicated operation or operations....
 P.4.84: In Exercises 8390, perform fire indicated operation or operations....
 P.4.85: In Exercises 8390, perform fire indicated operation or operations....
 P.4.86: In Exercises 8390, perform fire indicated operation or operations....
 P.4.87: In Exercises 8390, perform fire indicated operation or operations....
 P.4.88: In Exercises 8390, perform fire indicated operation or operations....
 P.4.89: In Exercises 8390, perform fire indicated operation or operations....
 P.4.90: In Exercises 8390, perform fire indicated operation or operations....
 P.4.91: As you (.:omplete more years of education, you c.an comll 011 a gre...
 P.4.92: As you (.:omplete more years of education, you c.an comll 011 a gre...
 P.4.93: The volume, V. of a rectangular solid with length J, width w. and h...
 P.4.94: The volume, V. of a rectangular solid with length J, width w. and h...
 P.4.95: In Exerdses 9596, write a po~wwmial in standard form that models, ...
 P.4.96: In Exerdses 9596, write a po~wwmial in standard form that models, ...
 P.4.97: What is a polynomial in x?
 P.4.98: Explain how to subtract polynomials.
 P.4.99: Explain how to multiply two binomials using the FOIL method. Give a...
 P.4.100: Explain how to find the product of the sum and difference o f two t...
 P.4.101: Explain how to square a binomial difference. Give an example with y...
 P.4.102: Explain how to find the degree of a polynomial in two variables.
 P.4.103: In Exercises 103106, determine whether each statement makes sense ...
 P.4.104: In Exercises 103106, determine whether each statement makes sense ...
 P.4.105: In Exercises 103106, determine whether each statement makes sense ...
 P.4.106: In Exercises 103106, determine whether each statement makes sense ...
 P.4.107: In Exercises 107110. determine whether each statement is true or f...
 P.4.108: In Exercises 107110. determine whether each statement is true or f...
 P.4.109: In Exercises 107110. determine whether each statement is true or f...
 P.4.110: In Exercises 107110. determine whether each statement is true or f...
 P.4.111: In Exercises 11113, perform the indicated operations. ((7x ~ 5) + ...
 P.4.112: In Exercises 11113, perform the indicated operations. ((3x ~ y) + 1 J
 P.4.113: In Exercises 11113, perform the indicated operations. (x" + 2)(x ...
 P.4.114: Express the area of the plane figure shown as a polynomial in stand...
 P.4.115: Exercises 115117 will help you prepare for tire mate,;al c.overed ...
 P.4.116: Exercises 115117 will help you prepare for tire mate,;al c.overed ...
 P.4.117: Exercises 115117 will help you prepare for tire mate,;al c.overed ...
Solutions for Chapter P.4: Polynomials
Full solutions for College Algebra  6th Edition
ISBN: 9780321782281
Solutions for Chapter P.4: Polynomials
Get Full SolutionsSince 117 problems in chapter P.4: Polynomials have been answered, more than 37147 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: College Algebra , edition: 6. Chapter P.4: Polynomials includes 117 full stepbystep solutions. College Algebra was written by and is associated to the ISBN: 9780321782281. This expansive textbook survival guide covers the following chapters and their solutions.

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

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

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

Determinant IAI = det(A).
Defined by det I = 1, sign reversal for row exchange, and linearity in each row. Then IAI = 0 when A is singular. Also IABI = IAIIBI and

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

Jordan form 1 = M 1 AM.
If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

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).

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

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

Permutation matrix P.
There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or 1) based on the number of row exchanges to reach I.

Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).