Operations with scientific notation.mp4

!±8± Operations with scientific notation.mp4

No rules. Just logical steps

Operations with scientific notation.mp4

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Factoring Polynomials - An Ultimate Approach

!±8± Factoring Polynomials - An Ultimate Approach

Factoring polynomials is a "must know" to understand algebra and score excellent grades in algebra. In this presentation we will explore the ultimate approach to factoring polynomials. Starting from factoring a monomial we will discuss every aspect of factoring polynomials.

To factor any kind of polynomial, knowledge of greatest common factor (GCF) is mandatory. If the students don't have the basic understanding of factoring numbers, they should review prime factorization of numbers first.

There are the following steps for factoring polynomials:

1. Find if there is any greatest common factor in the terms of given polynomial:

If the polynomial has the GCF, pull it out from each term of the polynomial by using the brackets. For example;

3a² + 6ab - 9a has "3a" as the GCF. Pull "3a" out as shown below to factor the polynomial;

3a (a + 2b - 3)

2. If the polynomial is a binomial (having two terms only), find if it is the difference of squares. Some times, by taking the GCF away, the binomial becomes the difference of squares. There is a special method for factoring difference of squares and I will discuss that in detail in my coming articles.

3. If the polynomial is a trinomial, again try to pull the greatest common factor away if you can. There is a special way to factor a trinomials and I am going to explain this topic alone in a separate article.

4. If the polynomial has four terms, then try to rearrange the terms and separate them into pairs of two's having greatest common factors. Take the greatest common factor out from each pair and see if you get two same brackets. For example; consider we have a polynomial, 4u² + 3a + 2u + 6au and we want to factor it.

There are four terms in the polynomial and there is no greatest common factor other than one. If we rearrange the terms and try to find the greatest common factor in the pairs of two terms, it might be possible to factor the polynomial that way.

So rewrite the polynomial by rearranging the terms as shown below:

4u² + 2u+ 3a + 6au

Look at the first pair "4u² + 2u" it has "2u" its GCF, pull it out as "2u (2u + 1)". Similarly factor the second pair as "3a (1+2u)". But, (1 + 2u) is same as (2u + 1), hence we can interchange them for simplicity.

= 2u (2u + 1) + 3a (2u+1)

Now, (2u + 1) is the common factor and pull it out as shown below:

= (2u + 1) (2u + 3a)

All the steps can be written together as follows;

4u² + 3a + 2u + 6au

= 4u² + 2u + 3a + 6au

= 2u (2u + 1) + 3a (2u+1)

= (2u + 1) (2u + 3a)

You can FOIL it to check your answer, if you get back the original polynomial.

Factoring Polynomials - An Ultimate Approach

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Getting to Know Vedic Arithmetic a Little Bit More

!±8± Getting to Know Vedic Arithmetic a Little Bit More

It is a common sentiment among humans, with a wee bit of emphasis on kids, that mathematics at its lowest and most raw form is simply hard. There are, however, different aspects of mathematics that we have to learn about more for they can be useful in developing strategies in dealing with real life situations. Vedic arithmetic is one of these less known mathematical concepts.

Basically, vedic arithmetic is a subset of vedic mathematics. This concept involves an algorithm operation which focuses on the algorithmic and correctness issues concerning numerals. There are questions concerning the label for this concept as critics continue to demand evidence supporting the concept's right to be referred to as vedic as well as mathematics. The lack of evidence is specific on the aspect concerning the connection of the whole system with that of the verdict sutras.

In its simplest form, verdict arithmetic involves numbers and numbers along with the other different basic concepts in mathematics such as the four major operations, square and square root, cubes, fractions and decimals. With the use of the equations, we can easily get to the answers to any numerical problems. Men of science usually make use of such equations to provide scientific calculations involving theories and methodologies in physical sciences. The use of the vedic formulas are helpful in making the calculation as fast as lightning and in order to end up with one liners for the answers.

The history of vedic arithmetic dates back a long time ago. Sri Bharati Krsna Tirthaji gave this name to refer to this mathematical concept as this is described as a form of ancient system rediscovered from the Vedas. There was a time when this concept was used to make sense of the way the mind works. It was a great help in getting the students directed towards the most appropriate way of solving the equation.

In our modern age of computers and calculators, a lot of people have shied away from developing skills of mental math, in particular, the basic methods of mental arithmetic. School children have asked why there is a need to learn about it when a calculator is readily available. This is a valid reason and can really catch the teacher off guard. This is however, a challenge left on the hands of our educators.

Getting to Know Vedic Arithmetic a Little Bit More

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