Binomials | Homework Help

Posts Tagged ‘binomials’

Zero-Factor Property

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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Factoring by Grouping

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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Completing the Square

Thursday, September 10th, 2009

A Guide to Completing the Square

Description

This video is a tutorial 0n how to solve quadratic equations by completing the square. Two example problems are provided in the video and worked through. The entire process of completing the square is explained in this video.

Overview

(x + a)^2 = x^2 + 2ax + a^2

You need to make your equation match up to this. Take the middle term and divide it by 2. That number is a. Square a – if you get the number on your trinomial, then this is a perfect square. You want it to be a perfect square. If it is not, you must get rid of the number on the end and move it to the other side by addition or subtraction. Then you will need to replace the number with a^2 – you will add this to both sides. You find out the value of a the same way you did earlier. You will eventually come up with something that looks like this:

(x + a)^2 = n

Now you will take the square root of both sides, and subtract a from both sides. Then you will be left with x, and it will tell you what x equal. Remember, when taking a square root you must put plus/minus in front of the square root! Just like in the quadratic formula, you need a +/- in your answer.

Tags: algebra, binomials, completing the square, Math, quadratic equation, square, square root, trinomial
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Factoring Quadratic Equations

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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FOIL Method

Tuesday, September 8th, 2009

How to Solve Equations by Using FOIL

Description

This video shows the correct way to multiply binomials together using the FOIL technique. A helpful hint for seeing if you matched up the terms correctly is given in the video. Content is laid out in an organized manner.

Overview

FOIL is a basic math function that stands for First, Outside, Inside, Last. It is like the Order of Operations – it gives you a set order to solve problems in. FOIL is used when you multiply two binomials together. Binomials are sets of parenthesis that have two added or subtracted numbers with variables in them. Here is an example of a problem that would need FOIL:

(a + b) (x – y)

You would use FOIL to multiply together different parts of the problem. We will highlight the parts of the problem in their correct order:

First: (a + b) (x – y)

Outside: (a + b) (x – y)

Inside: (a + b) (x – y)

Last: (a + b) (x - y)

Notice that the addition and subtraction signs are grouped with the last term in each set of parenthesis – this is very important if you expect to get the right answer. So, our problem can be simplified by writing it this way:

(a + b) (x – y) = (a * x) + (a * -y) + (b * x) + (b * -y)

Tags: algebra, binomials, F.O.I.L., First, FOIL, Inside, Last, Math, multiplication, Outside, parenthesis, terms
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