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October 15, 2008

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This is a part of the interactive online tutorial for Geometry learning with the help of audio visual lessons. It has been created to help you learn the concept, perception with explanations and includes solution to practice questions from the topic of 'Factoring binomials and polynomials’. The mini-lessons here include: Getting started, Factoring an expression of exponents with the same base, Factoring a quadratic into binomials, Factoring a quadratic using the perfect square method, Factoring a 3^{rd} degree polynomial.

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- Mathematics > Algebra

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This is a part of the interactive online tutorial for Geometry learning with the help of audio visual lessons. It has been created to help you learn the concept, perception with explanations and includes solution to practice questions from the topic of 'Factoring binomials and polynomials’. The mini-lessons here include: Getting started, Factoring an expression of exponents with the same base, Factoring a quadratic into binomials, Factoring a quadratic using the perfect square method, Factoring a 3^{rd} degree polynomial.

This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Getting started.

In this mini-lesson you'll learn how to factor the binomials and polynomials. It is an important step in solving problems in a good number of algebraic applications. In factoring polynomials, we determine all the terms that were multiplied together to get the given polynomial. We then try to factor each of the terms we found in the first step. This continues until we can’t factor anymore. For Example, here is the complete factorization of the polynomial

In this mini-lesson you'll learn how to factor the binomials and polynomials. It is an important step in solving problems in a good number of algebraic applications. In factoring polynomials, we determine all the terms that were multiplied together to get the given polynomial. We then try to factor each of the terms we found in the first step. This continues until we can’t factor anymore. For Example, here is the complete factorization of the polynomial

x^{4} – 16 = (x^{2} + 4)(x + 2)(x – 2)

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Algebra I. Click on the video below to go through it. If you like it, you can buy our online course in Algebra I by clicking here.

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This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Getting Started - Circles.

This mini-lesson introduces and walks you through the basic concepts of the circles. You'll learn it with the help of some examples, practice questions with solution,and using video explanation by the instructor that brings in an element of real-class room experience. You can see here the overview of the important basics of the circle, radius, chord etc.

A circle is the set of points that are equidistant from a special point in the plane. If the special point*O* is the center, it is called circle *O*. Some real-world examples of a circle are: a wheel, surface of a coin.

The radius is a line segment joining the center of the circle with a point on the circle. If any point*A* is on the circle with center *O*, then *OA* is the radius of circle. If you place two radii end-to-end in a circle, you would have the same length as one diameter. Thus the diameter of a circle is twice as long as the radius, E.g. a circle with 5 cms radius, will have 10 cms diameter.

A chord is a line segment joining two endpoints that lie on a circle. Further you may note that the diameter of a circle is the longest chord since it passes through the center and it can be stated every diameter is a chord, but not every chord is a diameter.

This mini-lesson introduces and walks you through the basic concepts of the circles. You'll learn it with the help of some examples, practice questions with solution,and using video explanation by the instructor that brings in an element of real-class room experience. You can see here the overview of the important basics of the circle, radius, chord etc.

A circle is the set of points that are equidistant from a special point in the plane. If the special point

The radius is a line segment joining the center of the circle with a point on the circle. If any point

A chord is a line segment joining two endpoints that lie on a circle. Further you may note that the diameter of a circle is the longest chord since it passes through the center and it can be stated every diameter is a chord, but not every chord is a diameter.

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Geometry. Click on the video below to go through it. If you like it, you can buy our online course in Geometry by clicking here.

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This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Factoring an expression of exponents with the same base.

In this mini-lesson you'll learn how to factor an expression of exponents with the same base. Generally speaking, for factoring exponents with the same base, we need to take a common factor out of the expression, and this factor is the base raised to the lowest exponent. For example, x^{2} is the common factor in the expression x^{2} + x^{6}, and hence the expression can be rewritten as x^{2}(1 + x^{4}).

In this mini-lesson you'll learn how to factor an expression of exponents with the same base. Generally speaking, for factoring exponents with the same base, we need to take a common factor out of the expression, and this factor is the base raised to the lowest exponent. For example, x

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Algebra I. Click on the video below to go through it. If you like it, you can buy our online course in Algebra I by clicking here.

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This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Factoring a quadratic into binomials.

This mini-lesson shows you how to factor a quadratic into binomials. As is the case in Algebra many times, the overview provided here in text might seem a little complicated, but don't worry -- it will be easy to follow once you hear the instructor explain it in the video provided. Some quadratics can be factored into two identical binomials. Such quadratics are called perfect square trinomials. As quadratic expression is the product of two binomials, factoring a quadratic means breaking the quadratic back into its binomial parts. Here factoring is done using the rule of LIOF (FOIL in reverse). A couple of general rules to keep in mind:

This mini-lesson shows you how to factor a quadratic into binomials. As is the case in Algebra many times, the overview provided here in text might seem a little complicated, but don't worry -- it will be easy to follow once you hear the instructor explain it in the video provided. Some quadratics can be factored into two identical binomials. Such quadratics are called perfect square trinomials. As quadratic expression is the product of two binomials, factoring a quadratic means breaking the quadratic back into its binomial parts. Here factoring is done using the rule of LIOF (FOIL in reverse). A couple of general rules to keep in mind:

- The factoring of x
^{2}+ (a + b)x + ab will result into (x + a) (x + b). For example, the two factors of x^{2}+ 5x + 6 are (x + 2)(x + 3) - Another common type of algebraic factoring is called the difference of two squares: (x
^{2}– c^{2}) = (x + c) (x – c). For example: factors of x^{2}– 4 are (x + 2) (x – 2)

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Algebra I. Click on the video below to go through it. If you like it, you can buy our online course in Algebra I by clicking here.

Member Rating

Curriki Rating**'P'** - This is a trusted Partner resource P**'P'** - This is a trusted Partner resource

This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Factoring a quadratic using the perfect square method.

In this mini-lesson you'll learn how to factor a quadratic using the perfect square method. In such cases, not only can the quadratic can be factored into two expressions, but the expressions are the same. If we try to explain it in text, here is the general rule -- if we have a quadratic equation in which first and last term are both perfect squares and middle term is two times the square root of the first and last terms multiplied, it simplifies the quadratic to a binomial product or just one binomial raised to the second power. Reading this explanation in text is confusing to many of us -- just click on the video of our instructor explaining it and you'll understand the concept much more easily. Note that perfect square trinomials are often expressions of one of the following forms:

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Algebra I. Click on the video below to go through it. If you like it, you can buy our online course in Algebra I by clicking here.

In this mini-lesson you'll learn how to factor a quadratic using the perfect square method. In such cases, not only can the quadratic can be factored into two expressions, but the expressions are the same. If we try to explain it in text, here is the general rule -- if we have a quadratic equation in which first and last term are both perfect squares and middle term is two times the square root of the first and last terms multiplied, it simplifies the quadratic to a binomial product or just one binomial raised to the second power. Reading this explanation in text is confusing to many of us -- just click on the video of our instructor explaining it and you'll understand the concept much more easily. Note that perfect square trinomials are often expressions of one of the following forms:

- (x
^{2}+ 2ax + a^{2}), which is the same as (x + a)^{2} - (x
^{2}– 2ax + a^{2}), which is the same as (x – a)^{2}

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This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Factoring 3rd degree polynomial.

In this mini-lesson you'll learn with the help of several examples how to factor 3^{rd} degree polynomial into 2^{nd} degree polynomial and 1^{st} degree polynomial factor. As you know, if you write a polynomial as the product of two or more polynomials, you have factored it. It is fairly common to come across certain interesting forms of third degree polynomials, and here are a few rules to keep in mind in factoring them:

RULE 1: a^{3} + b^{3} = (a + b) (a^{2} – ab + b^{2})

RULE 2: a^{3} – b^{3} = (a – b)(a^{2} + ab + b^{2})

RULE 3: (x + y + z)(x^{2} + y^{2} + z^{2} – xy – yz – zx) = x^{3} + y^{3} + z^{3} – 3xyz.

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Algebra I. Click on the video below to go through it. If you like it, you can buy our online course in Algebra I by clicking here.

In this mini-lesson you'll learn with the help of several examples how to factor 3

RULE 1: a

RULE 2: a

RULE 3: (x + y + z)(x

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