Posts Tagged ‘factor’
Tuesday, November 10th, 2009
How to Make Factor Trees
Description
A detailed tutorial on how to make factor trees. Step by step tutorial including several examples on how to make factor trees for reference.
Overview
A factor tree is a type of tree diagram that splits numbers into their factors. It is a very useful method of simplification. First, start with a number and draw two lines from it. Two numbers that when multiplied equal your first number need to go there. A great number to start with is 2, if your number is an even number. you can start with any two numbers you like, provided they fit the guidelines, excluding anything paired with the number one – because then you won’t get anywhere. Then for each of your two numbers, if they are not simplified, you do the same process with them. Keep it up until you are down to simplified, or prime, numbers. You will know you have reached one when the only multiples are one and itself.
Tags: algebra, diagram, even, factor, itself, multiple, number, odd, one, prime, simplification, simplified, simplify, tree, two
Posted in Algebra | No Comments »
Tuesday, November 3rd, 2009
How to Find the Determinant
Description
A detailed tutorial on how to find the determinant. Step by step tutorial including several examples of finding the determinant for reference.
Overview
The determinant is a number that is associated with a square matrix. In a mathematical sense, the determinant is a scale factor for measure when the matrix is regarded as a linear transformation. The determinant is denoted by two bars on either side of the matrix, which can be confused with the absolute value of the matrix. The determinant is found by subtracting the products of the diagonals of the matrix, at least in a 2×2 matrix.
Tags: absolute, algebra, determinant, diagonal, factor, linear, matrices, matrix, product, scale, square, subtract, transformation, value
Posted in Algebra | No Comments »
Friday, October 30th, 2009
Introduction to the Euclidean Algorithm
Description
A detailed tutorial on the Euclidean algorithm. Step by step tutorial including several examples of the Euclidean algorithm for reference.
Overview
The Euclidean algorithm, sometimes referred to as Euclid’s algorithm, is the most efficient way of determining the greatest common factor of two numbers. The greatest common factor of two numbers is the largest number that divides them both evenly. The Euclidean algorithm is used in a series of steps – it follows a pattern that helps to find numbers and their factors with accuracy.
Tags: algebra, algorithm, common, divides, divisor, Euclid, Euclidean, evenly, factor, greatest, highest, negative, pattern, positive, remainder, steps
Posted in Algebra | No Comments »
Thursday, October 29th, 2009
How to Identify Coprime Numbers
Description
A detailed tutorial on identifying coprime numbers. Step by step tutorial including several examples of how to identify coprime numbers for reference.
Overview
Two numbers are considered to be coprime, or relatively prime, if they have no common positive factor other than 1, or if their greatest common divisor is 1. Sometimes the notation for perpendicular is used to say that a number A is coprime to another number B. The term coprime was invented because the numbers are prime together, but are not prime themselves. A prime number can be coprime with any number.
Tags: arithmetic, common, coprime, divisor, factor, greatest, notation, number, one, perpendicular, positive, prime, relatively
Posted in Arithmetic | No Comments »
Friday, October 9th, 2009
Overview of the Zero-Factor Property
Description
A detailed tutorial on solving problems using the zero-factor property. Step by step tutorial including several examples of the zero-factor property for reference.
Overview
The zero-factor property is very closely linked to solving quadratic equations by factoring. The zero-factor property takes place very close to the end of the problem. Once you have finished factoring, you are usually left with two binomials that are being multiplied. The zero-factor property involves setting each of these binomials equal to zero separately. This allowes you to solve for two different values of x. This works on anything that has more than one term with the same variable being multiplied together. The reason it works is that if you multiply anything by zero, the answer is zero. So all you need to do is set the separate parts equal to zero, and it is just as good as solving for the whole thing at one time.
Tags: algebra, binomials, equation, factor, factoring, Math, multiplication, Polynomials, property, quadratic, variable, zero, zero-factor
Posted in Algebra | No Comments »
Friday, September 11th, 2009
How to Factor by Grouping
Description
A detailed tutorial on how to factor by grouping. Step by step tutorial including several examples of how to factor by grouping for reference.
Overview
There are many different ways to factor, but one of the easiest ways is to factor by grouping. If you factor by grouping, it means that you are given (or split terms up into) 4 terms, and then split those 4 terms into two groups each consisting of 2 terms. Put parenthesis around these groups. Here’s an example:
axt + ax – at – a = (axt + ax) – (at – a)
Now you want to pull something out of the parenthesis. Whatever is left in your parenthesis should be exactly the same for both sets of parenthesis – it doesn’t matter if what was pulled out is different. Then, you create another set of two parenthesis and multiply them together – form two binomials that you could solve by FOIL, basically. In the first set goes what you pulled out of the parenthesis, for instance if you pulled a 4x out of one and a -5 out of the other, your first set would be (4x – 5). The second set of parenthesis is whatever was left in your parenthesis on your first set. Now you can solve the problem how you would normally would solve a factoring problem.
Tags: algebra, binomials, factor, factor by grouping, factoring, grouping, Math, multiplication, parenthesis
Posted in Algebra | No Comments »
Thursday, September 10th, 2009
How to Solve Quadratic Equations by Factoring
Description
This video shows how to factor quadratic equations. One sample problem is provided and worked through to give a clear explanation of the process.
Overview
A quadratic equation is probably the most well-known type of math problem, following the form ax^2 + bx + c = 0. Most people already know one way of solving these types of equations – the quadratic formula. But the quadratic formula is only one of 3 methods that can be used. The method discussed here is factoring. Factoring is what you call changing a trinomial (a quadratic equation) into two binomials. It is like a reverse method of FOIL. Since you starting out with an x^2 term, the first term in both of your binomials will be x. Now, you need to find the second terms for each of your binomials. You do this by looking for two numbers. These two numbers, when added, must equal the number in the middle term, and when multiplied, they must equal the number in the last term. You can use two negative, two positives, or two negatives and a positive. Let\’s say your numbers end up being -3 and 7. Then your binomials will be (x – 3)(x + 7). It doesn\’t matter if you put the 7 first or the 3 first. To solve, you set each part equal to 0. This means you will have x – 3 = 0 and x + 7 = 0. Then solve for x. Factoring is not possible for all quadratic equations, but it is easier than using the other methods if you think your equation can be factored.
Tags: algebra, binomials, factor, factoring, Math, quadratic equation, trinomial
Posted in Algebra | No Comments »
Tuesday, September 8th, 2009
How to Find the Greatest Common Factor
Description
This video demonstrates how to find the Greatest Common Factor of two numbers. An easy method for solving and one example problem are provided in the video.
Overview
The Greatest Common Factor, or GCF, is the largest factor that two numbers have in common. A factor is any positive number that when mulitplied by another positive number will equal the number you are trying to find factors for. For example, the number 2. The only factors of 2 are 1 and 2, because both 1 and 2 can be multiplied by another number to equal 2. When finding the GCF, you will be finding the factors for 2 or more numbers. and then comparing them. Your GCF is the highest number that they all have in common.
Tags: arithmetic, factor, factoring, GCF, Greatest Common Factor, Math
Posted in Arithmetic | No Comments »
