Posts Tagged ‘factoring’
Friday, October 9th, 2009
Indentifying Prime Polynomials
Description
A detailed tutorial on how to identify prime polynomials. Step by step tutorial including several examples of identifying prime polynomials for reference.
Overview
Prime polynomials are any polynomial that cannot be factored. Just like a number is prime if you can not break it down into two seperate whole numbers to multiply, a polynomial is prime if you cannot break it down into two separate binomials with whole numbers to multiply. When you run into a prime polynomial when trying to solve a quadratic equation, you cannot use the factoring method. what the factoring method does is split the polynomials into a binomial, which cannot be done to a prime polynomial. If you have a prime polynomial, you have to use the quadratic formula to solve it. At first, you can spot prime polynomials by attempting to factor it, but eventually you will be able to do it just by looking at it.
Tags: algebra, binomial, equation, factoring, formula, Math, multiply, number, polynomial, prime, quadratic, whole
Posted in Algebra | 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
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Friday, September 18th, 2009
An Introduction to Conjugate Expressions
Description
A detailed tutorial on the solving of conjugates and conjugate expressions. Step by step tutorial including several examples of how to solve conjugates and conjugate expressions for reference.
Overview
Conjugates are probably very familiar to you – if you have spent any time studying binomials, then you know what a conjugate is. However, there is one difference. A conjugate uses radicals, or square roots, instead of whole numbers. One number will be a whole number, and one number will be a radical for each binomial. You can solve them using the normal FOIL method that is used on binomials, and with the algebra tricks you learned for multiplying square roots.
Tags: algebra, binomial, conjugate, conjugate expressions, conjugates, factoring, FOIL, Math, quadratic equation, radicals, square roots, whole number
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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
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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
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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 »
Monday, August 17th, 2009
How to solve Quadratic Equations
Description
A detailed tutorial on the use of the Quadratic Formula to solve Quadratic Equations. Step by step tutorial including two example quadratic equations for reference. Knowledge of the Quadratic Formula and how to solve Quadratic Equations are a requirement for grade school algebra.
Overview
The quadratic formula follows the form 
.
In mathematics, a quadratic equation is a polynomial equation of the second degree. Quadratic equations follow the general form of 
where x represents a variable, and a, b, and c, represent coefficients and constants, with a≠0 .
The constants a, b, and c, are called respectively, the quadratic coefficient, the linear coefficient and the constant term or free term.
Tags: algebra, complete the square, factoring, Math, quadratic equation, quadratic formula
Posted in Algebra | 1 Comment »
