 5.2.1: To multiply the variables in monomials, retain each variable and __...
 5.2.2: To multiply 7x3 (4x5  8x2 + 6), use the ______________ property to...
 5.2.3: To multiply (5x + 3)(x2 + 8x + 7), begin by multiplying each term o...
 5.2.4: When using the FOIL method to find (x + 7)(3x + 5), the product of ...
 5.2.5: (A + B) 2 = ______________. The square of a binomial sum is the fir...
 5.2.6: (A  B) 2 = ______________. The square of a binomial difference is ...
 5.2.7: (A + B)(A  B) = ______________. The product of the sum and differe...
 5.2.8: If f(x) = x2  4x + 7, we find f(a + h) by replacing each occurrenc...
 5.2.9: 4x2 (3x + 2)
 5.2.10: 5x2 (6x + 7)
 5.2.11: 2y(y2  5y)
 5.2.12: 3y(y2  4y)
 5.2.13: 5x3 (2x5  4x2 + 9)
 5.2.14: 6x3 (3x5  5x2 + 7)
 5.2.15: 4xy(7x + 3y)
 5.2.16: 5xy(8x + 3y)
 5.2.17: 3ab2 (6a2b3 + 5ab)
 5.2.18: 5ab2 (10a2b3 + 7ab)
 5.2.19: 4x2y(3x4y2  7xy3 + 6)
 5.2.20: 3x2y(10x2y4  2xy3 + 7)
 5.2.21: 4xna3x2n  5xn + 1 2 xb
 5.2.22: 10xna4x2n  3xn + 1 5 xb
 5.2.23: (x  3)(x2 + 2x + 5)
 5.2.24: (x + 4)(x2  5x + 8)
 5.2.25: (x  1)(x2 + x + 1)
 5.2.26: (x  2)(x2 + 2x + 4)
 5.2.27: (a  b)(a2 + ab + b2 )
 5.2.28: (a + b)(a2  ab + b2 )
 5.2.29: (x2 + 2x  1)(x2 + 3x  4)
 5.2.30: (x2  2x + 3)(x2 + x + 1)
 5.2.31: (x  y)(x2  3xy + y2 )
 5.2.32: (x  y)(x2  4xy + y2 )
 5.2.33: (xy + 2)(x2y2  2xy + 4)
 5.2.34: (xy + 3)(x2y2  2xy + 5)
 5.2.35: (x + 4)(x + 7)
 5.2.36: (x + 5)(x + 8)
 5.2.37: (y + 5)(y  6)
 5.2.38: (y + 5)(y  8)
 5.2.39: (5x + 3)(2x + 1)
 5.2.40: (4x + 3)(5x + 1)
 5.2.41: (3y  4)(2y  1)
 5.2.42: (5y  2)(3y  1)
 5.2.43: (3x  2)(5x  4)
 5.2.44: (2x  3)(4x  5)
 5.2.45: (x  3y)(2x + 7y)
 5.2.46: (3x  y)(2x + 5y)
 5.2.47: (7xy + 1)(2xy  3)
 5.2.48: (3xy  1)(5xy + 2)
 5.2.49: (x  4)(x2  5)
 5.2.50: (x  5)(x2  3)
 5.2.51: (8x3 + 3)(x2  5)
 5.2.52: (7x3 + 5)(x2  2)
 5.2.53: (3xn  yn )(xn + 2yn )
 5.2.54: (5xn  yn )(xn + 4yn )
 5.2.55: (x + 3) 2
 5.2.56: (x + 4) 2
 5.2.57: (y  5) 2
 5.2.58: (y  6) 2
 5.2.59: (2x + y) 2
 5.2.60: (4x + y) 2
 5.2.61: (5x  3y) 2
 5.2.62: (3x  4y) 2
 5.2.63: (2x2 + 3y) 2
 5.2.64: (4x2 + 5y) 2
 5.2.65: (4xy2  xy) 2
 5.2.66: (5xy2  xy) 2
 5.2.67: (an + 4bn ) 2
 5.2.68: (3an  bn ) 2
 5.2.69: (x + 4)(x  4)
 5.2.70: (x + 5)(x  5)
 5.2.71: (5x + 3)(5x  3)
 5.2.72: (3x + 2)(3x  2)
 5.2.73: (4x + 7y)(4x  7y)
 5.2.74: (8x + 7y)(8x  7y)
 5.2.75: (y3 + 2)(y3  2)
 5.2.76: (y3 + 3)(y3  3)
 5.2.77: (1  y5 )(1 + y5 )
 5.2.78: (2  y5 )(2 + y5 )
 5.2.79: (7xy2  10y)(7xy2 + 10y)
 5.2.80: (3xy2  4y)(3xy2 + 4y)
 5.2.81: (5an  7)(5an + 7)
 5.2.82: (10bn  3)(10bn + 3)
 5.2.83: [(2x + 3) + 4y][(2x + 3)  4y]
 5.2.84: [(3x + 2) + 5y][(3x + 2)  5y]
 5.2.85: (x + y + 3)(x + y  3)
 5.2.86: (x + y + 4)(x + y  4)
 5.2.87: (5x + 7y  2)(5x + 7y + 2)
 5.2.88: (7x + 5y  2)(7x + 5y + 2)
 5.2.89: [5y + (2x + 3)][5y  (2x + 3)]
 5.2.90: [8y + (3x + 2)][8y  (3x + 2)]
 5.2.91: (x + y + 1) 2
 5.2.92: (x + y + 2) 2
 5.2.93: (x + 1)(x  1)(x2 + 1)
 5.2.94: (x + 2)(x  2)(x2 + 4)
 5.2.95: Let f(x) = x  2 and g(x) = x + 6. Find each of the following. a. (...
 5.2.96: Let f(x) = x  4 and g(x) = x + 10. Find each of the following. a. ...
 5.2.97: Let f(x) = x  3 and g(x) = x2 + 3x + 9. Find each of the following...
 5.2.98: Let f(x) = x + 3 and g(x) = x2  3x + 9. Find each of the following...
 5.2.99: f(x) = x2  3x + 7
 5.2.100: f(x) = x2  4x + 9
 5.2.101: f(x) = 3x2 + 2x  1
 5.2.102: f(x) = 4x2 + 5x  1
 5.2.103: (3x + 4y) 2  (3x  4y) 2
 5.2.104: (5x + 2y) 2  (5x  2y) 2
 5.2.105: (5x  7)(3x  2)  (4x  5)(6x  1)
 5.2.106: (3x + 5)(2x  9)  (7x  2)(x  1)
 5.2.107: (2x + 5)(2x  5)(4x2 + 25)
 5.2.108: (3x + 4)(3x  4)(9x2 + 16)
 5.2.109: (x  1) 3
 5.2.110: (x  2) 3
 5.2.111: (2x  7) 5 (2x  7) 3
 5.2.112: (5x  3) 6 (5x  3) 4
 5.2.113: In Exercises 113114, find the area of the large rectangle in two wa...
 5.2.114: In Exercises 113114, find the area of the large rectangle in two wa...
 5.2.115: In Exercises 115116, express each polynomial in standard formthat i...
 5.2.116: In Exercises 115116, express each polynomial in standard formthat i...
 5.2.117: In Exercises 117118, express each polynomial in standard form. a. W...
 5.2.118: In Exercises 117118, express each polynomial in standard form. a. W...
 5.2.119: A popular model of carryon luggage has a length that is 10 inches ...
 5.2.120: Before working this exercise, be sure that you have read the Blitze...
 5.2.121: Explain how to multiply monomials. Give an example.
 5.2.122: Explain how to multiply a monomial and a polynomial that is not a m...
 5.2.123: Explain how to multiply a binomial and a trinomial.
 5.2.124: What is the FOIL method and when is it used? Give an example of the...
 5.2.125: Explain how to square a binomial sum. Give an example.
 5.2.126: Explain how to square a binomial difference. Give an example.
 5.2.127: Explain how to find the product of the sum and difference of two te...
 5.2.128: How can the graph of function f g be obtained from the graphs of fu...
 5.2.129: Explain how to find f(a + h)  f(a) for a given function f.
 5.2.130: y1 = (x  2) 2 y2 = x2  4x + 4
 5.2.131: y1 = (x  4)(x2  3x + 2) y2 = x3  7x2 + 14x  8
 5.2.132: y1 = (x  1)(x2 + x + 1) y2 = x3  1
 5.2.133: y1 = (x + 1.5)(x  1.5) y2 = x2  2.25
 5.2.134: Graph f(x) = x + 4, g(x) = x  2, and the product function, f g, in...
 5.2.135: Knowing the difference between factors and terms is important: In (...
 5.2.136: I used the FOIL method to find the product of x + 5 and x2 + 2x + 1.
 5.2.137: Instead of using the formula for the square of a binomial sum, I pr...
 5.2.138: Specialproduct formulas have patterns that make their multiplicati...
 5.2.139: If f is a polynomial function, then f(a + h)  f(a) = f(a) + f(h) ...
 5.2.140: (x  5) 2 = x2  5x + 25
 5.2.141: (x + 1) 2 = x2 + 1
 5.2.142: Suppose a square garden has an area represented by 9x2 square feet....
 5.2.143: Express the area of the plane figure shown as a polynomial in stand...
 5.2.144: In Exercises 144145, represent the volume of each figure as a polyn...
 5.2.145: In Exercises 144145, represent the volume of each figure as a polyn...
 5.2.146: Simplify: (yn + 2)(yn  2)  (yn  3)2 .
 5.2.147: The product of two consecutive odd integers is 22 less than the squ...
 5.2.148: Solve: 3x + 4 10. (Section 4.3, Example 6)
 5.2.149: Solve: 2  6x 20. (Section 4.1, Example 2)
 5.2.150: Write in scientific notation: 8,034,000,000. (Section 1.7, Example 2)
 5.2.151: Replace each boxed question mark with a polynomial that results in ...
 5.2.152: (x  5)(x2 + 3)
 5.2.153: (x + 4)(3x  2y)
Solutions for Chapter 5.2: Multiplication of Polynomials
Full solutions for Intermediate Algebra for College Students  6th Edition
ISBN: 9780321758934
Solutions for Chapter 5.2: Multiplication of Polynomials
Get Full SolutionsIntermediate Algebra for College Students was written by and is associated to the ISBN: 9780321758934. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Intermediate Algebra for College Students, edition: 6. Since 153 problems in chapter 5.2: Multiplication of Polynomials have been answered, more than 14908 students have viewed full stepbystep solutions from this chapter. Chapter 5.2: Multiplication of Polynomials includes 153 full stepbystep solutions.

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!

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

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.

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

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

Dimension of vector space
dim(V) = number of vectors in any basis for V.

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

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

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.

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

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.

Matrix multiplication AB.
The i, j entry of AB is (row i of A)·(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

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.

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).

Row picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.

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.

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.
I don't want to reset my password
Need help? Contact support
Having trouble accessing your account? Let us help you, contact support at +1(510) 9441054 or support@studysoup.com
Forgot password? Reset it here