Common Factoring: Find out the GREATEST COMMON FACTOR of each term and factor it out. Using Grouping:
Sometimes, a polynomial will have no common factor for all the terms. Instead, we can group together the terms which have a common factor. When you use the Grouping Method:
* When there is no factor common to all terms
* When there is an even number of terms.
Example:

The polynomial x3+3x2−6x−18 has no single factor that is common to every term. However, we notice that if we group together the first two terms and the second two terms, we see that each resulting binomial has a particular factor common to both terms.

Factor x2 out of the first two terms, and factor −6 out of the second two terms. x2(x+3) −6(x+3)
Now look closely at this binomial. Each of the two terms contains the factor (x+3). Factor out (x+3).
(x+3) (x2−6) is the final factorization.
x3+3x2−6x−18= (x+3) (x2−6)

Factoring Trinomials:

Notice that the first term in the resulting trinomial comes from the product of the first terms in the binomials: x⋅x=x2. The last term in the trinomial comes from the product of the last terms in the binomials: 4⋅7=28. The middle term comes from the addition of the outer and inner products: 7x+4x=11x. Also, notice that the coefficient of the middle term is exactly the sum of the last terms in the binomials: 4+7=11.

Method of Factoring
1. Write two sets of parentheses:( ) ( ).
2. Place a binomial into each set of parentheses. The first term of each binomial is a factor of the first term of the trinomial. 3. Determine the second terms of the binomials by determining the factors of the third term that when added together yield the coefficient of the middle term.

...block to overcome its state of inertia. A body travelling on an inclined plane due to its weight has an angle of repose, wherein it has a uniform sliding motion. There is no acceleration taking place when the block slides uniformly. No matter what vertical height or horizontal distance is used, the angle of repose will remain the same. The tangent of the angle of repose is always equal to the coefficient of friction of the block.
Coefficient of friction denoted by μ is determined the formula μ=FN f=Friction force, N=normal force. The value of μ has no units since it only serves as a factor between F and N. In order to obtain a constant value for the μ, one has to consider state of equilibrium for the object being experimented. We also took note of the fact that 0 < u < 1.
In cases which there is an angle of repose, all forces involved are being translated with accordance to the surface’s inclination. The weight will now have components that contribute to the sliding of the object. If we have the angle of repose as θ, the components of W contributed to the object in sliding motion are Wsinθ, parallel to the surface and Wcosθ, perpendicular to the surface. Since the system is in equilibrium, Wsinθ is also equaled by the frictional force, while Wcosθ is also equaled by the normal force. In determining μ, it would be μ=FN=WsinθWcosθ=tanθ. Since the θ for the value of μ is also the θ of inclination, therefore in correlation, we can relate μ as equal to the...

...
The case between Beauty and Stylish involves concept of a valid contract, pre-contractual statements, express term and misrepresentation.
A valid contract is established between Beauty and Stylish when an offer is accepted and there is intention for both parties to create legal relations. An offer refers to the expression of willingness of the offerer to be contractually bound by an agreement if his or her offer is properly accepted. It has to be clear and certain in terms. It must also be communicated to the offeree before it is being accepted. In addition, the acceptance has to be unqualified, unconditional and made by a positive act. In the case of Beauty and Stylish, a positive act refers to the signing of the contract. All terms of the offer must be accepted without any changes and cannot be subjected to any condition, taking effect only upon fulfillment of that condition. When Beauty and Stylish enter into the agreement, they must intend to bind and bound legally to each other by their agreement. This is the intention to create legal relations between two parties. In the meanwhile, this contract must possess consideration. A contract must therefore be a two-sided affair, with each side providing or promising to provide something of value in exchange for what the other is to provide.
Every contract, whether oral or written, contain terms. The terms of a contract set out the rights and duties of the parties. Terms are the promises and undertakings given by each...

...pp. 737-738. Please note that entries must be alphabetized and that the first line of each entry should be flush with the margin, but all successive lines should be indented 5 spaces. This is called a “hanging indent.”
Assignment: Write an essay about a concept that interests you and that you want to study further. When you have a good understanding of the concept, explain it to your readers, using definition, comparison and contrast, cause and effect and/or any other appropriate rhetorical strategies, considering carefully what your readers already know about the topic and how your essay might add to what they know. Be sure to support your explanation with specific facts and examples.
You are required to cite at least seven (7) sources. Two (2) of these may be approved websites and four (4) must be articles originally published in a reputable magazine, newspaper or peer-edited journal. Use the library’s online databases to find such articles. A handout posted on Bb under Content explains how to do this, and we will have a day in the computer lab, or classroom, where I walk you through the process. Please note that, without an individual exception approved by me, you may use no more than two (2) books. All information taken from your sources must be properly documented, using MLA style parenthetical citations along with a Works cited page. SMG, Ch. 27 shows you how to do this. If you have questions at any stage of the process,...

...Factoring is the process of writing a polynomial as the product of two or more polynomials. General Strategy for Factoring Factor out the greatest common factor If the polynomial has two terms, determine whether it matches the pattern of one of the special products Difference of two squares a INCLUDEPICTURE mhtmlfile//ZFactoring.mhthttp//www.okc.cc.ok.us/maustin/Factoring/Image41.gif MERGEFORMATINET - b INCLUDEPICTURE mhtmlfile//ZFactoring.mhthttp//www.okc.cc.ok.us/maustin/Factoring/Image193.gif MERGEFORMATINET (a b)(a b) Difference of two cubes a INCLUDEPICTURE mhtmlfile//ZFactoring.mhthttp//www.okc.cc.ok.us/maustin/Factoring/Image194.gif MERGEFORMATINET - b INCLUDEPICTURE mhtmlfile//ZFactoring.mhthttp//www.okc.cc.ok.us/maustin/Factoring/Image195.gif MERGEFORMATINET (a b)(a INCLUDEPICTURE mhtmlfile//ZFactoring.mhthttp//www.okc.cc.ok.us/maustin/Factoring/Image196.gif MERGEFORMATINET ab b INCLUDEPICTURE mhtmlfile//ZFactoring.mhthttp//www.okc.cc.ok.us/maustin/Factoring/Image196.gif MERGEFORMATINET ) Sum of two cubes a INCLUDEPICTURE mhtmlfile//ZFactoring.mhthttp//www.okc.cc.ok.us/maustin/Factoring/Image197.gif MERGEFORMATINET b INCLUDEPICTURE mhtmlfile//ZFactoring.mhthttp//www.okc.cc.ok.us/maustin/Factoring/Image198.gif MERGEFORMATINET (a b)(a INCLUDEPICTURE...

...On this page we hope to clear up problems you might have with polynomials and factoring. All the different methods of factoring and different things such as the difference of cubes are covered. Click any of the links below or scroll down to start gaining a better understanding of polynomials and factoring.
Combining like terms
Multiplication of polynomials
FactoringFactoring by grouping
Sums and differences of cubes
Quiz on Polynomials and Factoring
When terms of a polynomial have the same variables raised to the same powers, the terms are called similar, or like terms. Like terms can be combined to make the polynomial easier to deal with. Example:
1. Problem: Combine like terms in the following
equation: 3x2 - 4y + 2x2.
Solution: Rearrange the terms so it is easier
to deal with.
3x2 + 2x2 - 4y
Combine the like terms.
Probably the most important kind of polynomial multiplication that you can learn is the multiplication of binomials (polynomials with two terms). An easy way to remember how to multiply binomials is the FOIL method, which stands for first, outside, inside, last. Example:
1. Problem: Multiply (3xy + 2x)(x^2 + 2xy^2).
Simplify the answer.
Solution: Multiply the first terms of each bi-
nomial. (F)
3xy * x2 = 3x3y
Multiply the outside terms of each binomial....

...squares binomials as separate factors?
distribution
in what conditions can a factored expression be factored further?
Greatest Common Factor
A greatest common factor of two or more terms is the largest factor that all terms have in common. The greatest common factor of a polynomial should be factored out first before any further factoring is completed.
Example:
3r6+27r4+15r2=3r2(r4+9r2+5)
When multiplying variables, add the exponents.
r^2•r^4=rr•rrrr=r6
Whenfactoring a GCF, subtract the exponents.
To factor r^2 from r^6: r^6−2=r^4
rrrrrr=(rr)(rrrr)=r2(r4)
Difference of Squares Binomials
A difference of squares binomial includes a perfect square term subtracted by another perfect square term.
Pattern:
a^2−b^2=(a+b)(a−b)
Example:
r^2−4=(r+2)(r−2)
Perfect Square Trinomials
A perfect square trinomial is a polynomial of three terms where the first and last terms are perfect squares and the middle term is twice the product of the square roots of those terms.
Pattern:
a^2+2ab+b^2=(a+b)^2 OR a^2−2ab+b^2=(a−b)^2
Example:
r^2+12r+36=(r+6)^2 r^2−12r+36=(r−6)^2
Check your factors to see if they can be factored further
Sometimes after an initial factoring, the remaining terms can be factored further.
Example:
t^8−81
This is a difference of squares.
(t^4+9)(t^4−9)
The factor(t^4−9) is also a difference of squares.
(t^4+9)(t2+3)(t^2−3)
Even though there are even powers here, these are not special products so this is factored completely....

...1
Class X Mathematics Chapter 2: Polynomials Chapter Notes Top Definitions 1. A polynomial p(x) in one variable x is an algebraic expression in x of the form p(x) = anxn an1xn1 an 2 xn 2 ........ a2 x2 a1x a0 , where (i) a0 , a1, a2......an are constants (ii)x is a variable (iii) a0 , a1, a2......an are respectively the coefficients of xi. (iv) Each of anxn an1xn1, an 2 xn 2 ,........a2 x 2 , a1x, a0 , with an 0, is called a term of a polynomial. 2. 3. 4. The highest exponent of the variable in a polynomial is called the degree of the polynomial. A polynomial of degree one is called a linear polynomial. It is of the form ax + b. Examples: x-2, 4y+89, 3x-z. A polynomial of degree two is called a quadratic polynomial. It is of the form ax2 + bx + c. where a, b, c are real numbers and a 0 Examples: x2-2x+5, x2-3x etc. A polynomial of degree 3 is called a cubic polynomial and has the general form ax3 + bx2 + c x +d. For example: x3 2 x 2 2 x 5 etc. A real number k is said to be the zero of the polynomial p(x) if p (k) = 0.
5.
6.
Top Concepts: 1. 2. 3. 4. The graph of a polynomial p(x) of degree n can intersects or touch the x axis at atmost n points. A polynomial of degree n has at most n distinct real zeroes. The zero of the polynomial p(x) satisfies the equation p(x) = 0. For any linear polynomial ax+b, zero of the polynomial will be given by the expression (-b/a).
2
5. 6. 7. 8. 9. 10. The number of real zeros of...

...Chapter 11
Four Decades of the Defence of
Australia: Reflections on Australian
Defence Policy over the Past 40 Years
Hugh White
The serious academic study of Australian defence policy can be said to have
begun with the publication of a book by the SDSC’s founder, Tom Millar, in
1965. The dust jacket of that book, Australia’s Defence, posed the following
question: ‘Can Australia Defend Itself?’ Millar thus placed the defence of Australia
at the centre of his (and the SDSC’s) work from the outset. Much of the SDSC’s
effort over the intervening 40 years, and I would venture to say most of what
has been of value in that effort, has been directed toward questions about the
defence of the continent. This has also been the case for most of the work by
Australian defence policymakers over the same period. In this chapter I want
to reflect on that work by exploring how the idea of the ‘defence of Australia’
has evolved over that time, and especially how its role in policy has changed,
from the mid-1960s up to and including the most recent comprehensive statement
of defence policy, Defence 2000: Our Future Defence Force.
This is no dry academic question. The key question for Australian defence
policy today is how we balance priority for the defence of Australia against
priority for the defence of wider strategic interests. The starting point for that
debate is the policies of the 1970s and 1980s, which placed major emphasis on
the defence of the continent....

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