? Demonstrate that factoring a polynomial is the reverse of multiplying a polynomial.
? Use greatest common factor (GCF) to factor monomials out of quadratic trinomials.
? Factor single-variable polynomials by grouping.
? Factor quadratic trinomials.
? Factor multivariate polynomials by grouping.
? Factor differences of squares.
? Factor complete squares.
? Solve quadratic equations using the zero factor property.
? Apply the Pythagorean Theorem to real-life problems.

40. 16x2Z, 40xz2, 72z3

68. 15x2y2 -9xy2 + 6x2y

72. a(a + 1) -3(a +1)

16. 9a2 - 64b2

62. x3y + 2x2y2 + xy3

64. h2 - 9hs + 9s2

102. 3x3y2 - 3x2y2 + 3xy2

18. 2x2 + 11x + 5

26. 21x2 + 2x - 3

88. a2b + 2ab - 15b

36. m4 - n4

66. 8b2 + 24b + 18

72. 3x2 -18x - 48

82. 9x2 +4y2

18. 2h2 - h - 3 = 0

32. 2w(4w + 1) = 1

98. Avoiding a collision. A car is traveling on a road that
is perpendicular to a railroad track. When the car is
30 meters from the crossing, the car's new collision
detector warns the driver that there is a train 50 meters
from the car and heading toward the same crossing. How
far is the train from the crossing?

104. Venture capital. Henry invested $12,000 in a new
restaurant. When the restaurant was sold two years
later, he received $27,000. Find his average annual
return by solving the equation 12,000(1 _ r)2 _
27,000.

Team :

100. Demand for pools. Tropical Pools sells an aboveground
model for p dollars each. The monthly revenue for this
model is given by the formula

R(p)=0.08p2 +300p.
Revenue is the product of the price p and the demand
(quantity sold).
a) Factor out the price on the right-hand side of the
formula.
b) Write a formula D(p) for the monthly demand.
c) Find D(3000).
d) Use the accompanying graph to estimate the price at
which the revenue is maximized. Approximately how
many pools will be sold monthly at this price?

Let A= (1 0 -1 and b=(1
1 2 1 1
1 1 -3 1
0 1 1) 1)
1) Determine the QR factorization of A
2) Use the QR factors in 1) to determine the lease squares solution to Ax=b. Ax=b is the solution related to Rx=Q^Tb

Please see the attached file for the fully formatted problems.
22 problems about ...
factorization
GCF
LCM
fractions
simplest form
mixed fractions
word problems
decimals
percent
exponents
absolute value

** Please see the attached file for the complete problem description **
Need help with attached problems
Let p an odd prime, show that either p == 1 mod 4 or p == 3 mod 4.
Show that no prime of the form 4n + 3 can be written as a2 + b2 for some integers a and b.
Show that 17 is not prime in J[i], by finding a factorizati

Total of 29 problems that look like these
What is the degree of f(x) =3x^6 +4x^2 +x - 1
What is the leading coefficient of f(x) = 3x^6 +x^2 +x - 1
Write a polynomial in simplest form with roots 5i and -5i
Solve (x - 1)(x - 2) ? 0
x - 3

Can someone explain why the first two answers are the same? Can a person do the foil to get them equal? Can we also try:
(a^3 - b^3)=(a-b)(a^2+ab+b^2)
(a^4-b^4)= (a-b)(a^3 + a^2b + ab^2 +b^3)
Can we find a^n - b^n = (a-b)(...)?

Show that every positive integer n can be written in the form n = ab where a is square-free and b is a square. Show that b is thi the largest square dividing n. (A square-free integer is an integer that is not divisible by any square > 1).

If R is a unique factorization domain and if a and b in R are relatively prime
(i.e.,(a,b) = 1), whenever a divides bc, then a divides c.
That is, if R is a unique factorization domain and if a and b in R are relatively prime
(i.e., (a,b) = 1), whenever a divides bc then a divides c.

1) Apply the Gram-Schmidt process to a_1 = (0 0 1)^T, a_2 = (0 1 1)^T, and a_3 = (1 1 1)^T and write the result in the form A=QR
2) Apply the Gram-Schmidt process to the vectors above in reverse order:
in the form A = QR. where a_1= (1 1 1)^T, a_2=(0 1 1)^T, and a_3=(0 0 1)^T

Form an LU factorization of the following symmetric matrix to show that it is not positive definite.
4 1 -1 2
1 3 -2 -1
-1 -2 1 6
2 -1 6 1
Using a little ingenuity we can find a non-zero vector such as x^T = ( 0 1 1 0) that does not satisfy the requirement x^T Ax > 0.

Please provide steps so that I can understand the process of finding sufficient statistics using the Factorization Theorem.
Let X1, X2,...,Xn be a random sample from the normal distribution N(0,THETA), 0 < THETA < +infinity. Show that "(the sum from 1 to n of (Xi^2))" is a sufficient statistic of THETA.
What is inside eq