Below is the next post in the series on how to factorize quadratic trinomials. Now on we included one difficulty level where we have to pull out the greatest common factor before applying the other factoring techniques.
So far in the series of factoring polynomials following have been explored and at this stage it needs to be go over all the steps.
I always ask my students to make sure they know all the above concepts before moving further into factoring polynomials.
"The Compendious Book on Calculation by Completion and Balancing," is the great work that brought us our modern system of numerals and mathematics. Thanks to the excellent intelligence, scholarship and organizational skills of several people who perceived some of the impracticalities of the European model and its transmission, tremendous tools were compiled and made convenient, such that today, we each use these methods in some way, on a daily basis.
The decimal and the number zero are first examples of those tools.
Also was a simple method for teaching what we now call algebra, or al-jabr, which was codified by a man named Al-Khwarizmi. He was also known in Latin, as Algoritmi, the source of the word algorithm, and is the author of the above title. His fascination and skill came from studying and practicing the pattern based system known as Vedic math,
When it comes to memorizing the times tables I have seen kids moving away from it and they feel it very hard. But their are few tricks which can be utilized to memorize times tables.
Below is a pattern I used to memorize 9 times table when I was young. The trick is that all the multiples of 9 have the sum of their digits equal to 9. For example 3 times 9 is 27 and if we look at 27 and add 2 and 7 we get 9 as the answer. Similarly 6 times 9 is 54 and sum of digits of 54 is 9 again.
There is a little explanation on these tricks to memorize 9 times table.
Many people use the 10 fingers of the hands to memorize it easily. Below is a cool video explaining the concept.
This is the 4th post in the series on how to factorize quadratic trinomials. This is the last one in its category where we didn't need to take out the greatest common factor from the 3 terms of the given trinomial and the coefficient of the quadratic term (x²) is "1".
Below is an example with brief explanations:
Place value is one of the key math foundational skills which needs to be learned in very early ages (grade 2 to grade 5). This post is all about the place value for beginners. Even parents can help their toddlers learn place value after going over the material given in this post.
Concept of Place Value: Place value is base ten system of counting. Ones (units) are bundled into Tens, then tens into 10 tens to get hundreds and then 10 hundreds to get thousands and so on.
First of all we need to understand the need for place value system. The following lessons explain it a little;
Continuing our journey to explore factoring quadratic trinomials, this is the third post in the series. Again factoring the such a quadratic trinomial is very easy if the students know how to find all the factors of a given number and basic integers rules.
Below is the explanation to find factors of a given trinomial:
Please let me know in the comment section if you need pdf copies for the practice on the concept.
A Möbius strip is a one-dimensional object you can create in your own home. You do this by taking a long strip of paper, creating a loop, and twisting one end over 180° before connecting the ends.
But that creates a 3-dimensional object I can see and hold, you might say. WRONG! There is only one side, and only one edge. But that is only where the strangeness begins. Observe what happens when you cut a Möbius strip...
Many reports and numbers have been grouped around Bitcoin since as early as 2013.
What Wall Street and even Bitcoin holders have failed to realize is the absolutely atmospheric-shattering cap this market has on it.
"To the moon." became a popular catch phrase among bitcoin supporters and I'm here to tell you today and you can mark my words - that does not even begin to describe the world changing economic and political parity we are about to experience in the very near future of planet Earth.
Let's rephrase it:
Prime Numbers: Numbers which have only two factors are called the prime numbers. These two factors have to be number itself and the number one. For example; 2, 3, 5, 7, 13, 17, 19, 23 and 29 are all prime numbers. Can find more prime numbers below 100?
2 is only even number which is prime. 1 is not a prime number as it has only one factor which is itself.
Composite Numbers: Numbers which have more than two factors are called the composite numbers. Obviously numbers which are not prime numbers are composite numbers.
For example; 4, 6, 8, 9, 10, 12, 14, 15 etc. are all composite numbers. Can you find more composite numbers?
Don’t get confused with even and odd; prime and composite. Even numbers are divisible by 2 and odd numbers are n
I have been teaching math for a couple of months and I've learned that teaching is hard work! I have had the benefit of loving math and enjoying new intellectual challenges.
What happens when a child has no interest in math? You end up having to make things really fun. The lesson becomes an excercise in finding what the student enjoys and building a bridge between that passion and some mathematical concept.
I had the added challenge of being in classrooms that were next door to students who were testing all day and needed a silent environment.
The best I could do was create math lessons on folding paper. Folding paper is pretty silent, and you end up with a tactile result and the pride of procuding something in the class hour.
So I did some math... if someone makes a Mr. Fusion... and you use one can of beer... the potential energy...
E=MC^2 so… we assume 371.38g of beer (I took the weight of 12 fluid ounces of water and did some guestimation since beer isn't pure water)
7.9775e+3 kilotons of TNT
7.9775 megatons of TNT
3.16362398 x 10^13 BTU
9.27166665 × 10^9 kwh or 7.97753345 × 10^12 kilocalories
Which is 9,271,666,650 kwh where the U.S. used an estimated 3.741 trillion kWh in 2009. So .002% of the U.S. energy consumption for 2009. Now... that's 1.243350979e+10 horsepower hours.
It’s also 9,271.66665 jigawatts Marty
So I was thinking about what such a device as the Mr. Fusion would mean as far as power for space travel...
SpaceX's Falcon 9 rocket carries 395,700kg of fuel (119,100 Kilograms of Rock
I wrote an article on combining like terms in algebra long ago and want to share. We need to know the basic algebra, such as variables, coefficients, algebraic expressions and polynomials to be able do it. In this representation I am going to explain how to combine like terms in a polynomial or an algebraic expression.
Like terms in a polynomial contain the same variable. For example “3a” and “6a” are the like terms because both terms contain the same variable “a”. On the other hand “3a” and “6b” are not the like terms as they contain the different variables “a” and “b
Divisible means a number completely divide another number and gives zero remainder. We can tell very easily that if 2 or 3 or 5 will completely divide a given number without doing the long division.
Below are the Divisibility Rules (tests) starting at the test for divisibility by 2 and ending at test for divisibility by 10:
Algebraic Expressions and Equations
We created an algebraic equations in two variables using a very simple example from a daily life activity in my previous post. If you missed that post please click the link below to see it.
In that example we created a simple algebraic equation as below:
Arthur’s Earnings = 60 + 25 x number of lawns mowed
In above equation, there are two variable (changing or unknown activities). One is Arthur’s earnings and the other is number of lawns mowed by him. We used lower case letters to represent these variables as shown below:
Arthur’s Earnings = e
Number of lawns mowed = n
Then our equation became
There are many reasons which make math a hard and most hated subject by the kids. One of the most important reasons is the insufficient knowledge of basic math concepts such as least common multiple or (lcm) and greatest common factor (gcf). Many students don’t care about these basic concepts when there is a right time to learn these basic concepts.
Image Credit: http://kbreuerclasswebsite.weebly.com
In grade three or four students start to learn multiples. Once students start learning multiplication and get comfortable with it, they should learn about multiples.
Multiples are other form of times and actually the word “times” can be interchanged with the word “multiples”. It is the further use of multiples which makes
We all probably had hard times in school with maths and equations but what if I told you it can do things like this:
With only some simple Equations:
x(t) = ((-1/38 sin(17/11 - 37 t) - 1/30 sin(31/21 - 35 t) - 1/25 sin(16/11 - 33 t) - 1/24 sin(16/11 - 31 t) - 1/28 sin(3/2 - 29 t) - 1/31 sin(10/7 - 24 t) - 1/23 sin(3/2 - 22 t) - 1/78 sin(12/11 - 20 t) - 1/8 sin(11/7 - 15 t) - 2/9 sin(14/9 - 13 t) - 3/7 sin(14/9 - 11 t) - 1/5 sin(11/7 - 9 t) - 7/15 sin(14/9 - 7 t) -... (continues ~70 lines)
Okay maybe not that easy but you get the idea. You can even check it yourself on wolframalpha:
The equation is at the bottom.
Now discover something even more interesting, is there a equation that can
draw itself? Well it took some time but in 2001 Juff Tupper discov