Algebra For Beginners - What Does It Means To Factor and Why Is It So Important In Algebra?

Algebra has become a "must take" course in high school. However, while technology keeps advancing and Algebra becomes a course in which everyone needs to be proficient, student success rates remain consistently low. There are many reasons for this, but one of those reasons is that students do not become proficient in the vocabulary part of mathematics. In fact, math students complain loudly if given vocabulary and spelling quizzes, claiming, "this isn't English class!" Students fail to understand that if they do not master the vocabulary, they will perform badly on tests because they won't understand what the directions are telling them to do. The instruction "Factor..." is a prime example of this problem.

What Is Factoring?

In simplest terms, the process of "factoring" or the verb "to factor" means to re-write an algebraic expression in terms of multiplication. Factoring is a process that is used throughout Algebra; but if you ask even the top students what the verb "to factor" means, very few will answer correctly.

Students understand factoring from arithmetic. Ask students to "factor 6," they will know to write 6 = 2 x 3. Asking students to "factor 12" may result in 12 = 2 x 6 or 12 = 3 x 4, and a few students might continue factoring to 12 = 2 x 6 = 2 x 2 x 3 = 2^2 x 3. These students know to factor to a product of prime numbers.

However, asking an Algebra class early in the year to factor the expression 2x + 2y will get you a room full of blank stares. They do not transfer their knowledge of the word "factor" from arithmetic to Algebra. For Algebra students to get proficient at the terminology, we need to give our students many examples of what we are doing; and we need to have our students saying and explaining definitions and properties and giving examples OUT LOUD.

Initially, factoring in Algebra relies heavily on the Distributive Property. Surprisingly, students seem to quickly understand and effectively use the distributive property for factoring two uncomplicated terms. When looking at 2x + 2y, students generally recognize the common multiplier of 2. Then they learn to use the Distributive Property to re-write the expression using multiplication. 2x + 2y = 2(x + y).

Students have a little more difficulty as the terms get more complicated and/or the number of terms increases; but with several examples and practice, students can factor expressions like: 3a + 9ab - 15ac. Each term shares both 3 and a. Again, using the Distributive Property, the expression 3a + 9ab - 15ac becomes 3a(1 + 3b - 5c) when re-written as multiplication.

Note: One of the best things about factoring is that it can be easily checked by performing the multiplication to verify that the result is the original expression.

Now that we know WHAT factoring is, we need to understand the reasons WHY to factor.

Why Do We Need To Factor?

There are two main uses for factoring: (1) reducing fractions, and (2) solving equations.

Reducing Fractions:

As with factoring, students learn to reduce fractions in arithmetic. 12/14 = (2 x 6)/(2 x 7) = (2/2)(6/7) = 1(6/7) = 6/7.

Making the transfer of that knowledge to Algebra often causes trouble; but just as in arithmetic, reducing algebraic fractions uses factoring and the fact that x/x = 1.

Reduce: (3a + 9ab) / (3a^2 + 15ab).

This fraction becomes 3a(1 + 3b) / 3a(a + 5b) = (3a/3a) ((1 + 3b)/(a + 5b)) = 1 ((1 + 3b)/(a + 5b)) = (1 + 3b)/(a + 5b).

Solving Equations:

Some algebraic equations can be solved (which means to find the values that make the equation true) by first moving all the terms to one side of the equal sign. This leaves zero on the other side. Then, if possible, the algebraic expression is factored. Then the fact that if ab = 0, then either a = 0 or b = 0 allows us to find solutions.

Solve: a^2 = 3a.

This equation becomes a^2 - 3a = 0. Then factoring gives us a(a - 3) = 0. So either a = 0 or (a - 3) = 0. This tells that we have two values that make the original equation true: 0 and 3.

For every example in this article, the factoring method used has been the Distributive Property. There are, however, other methods for factoring different types of expressions. Those will be discussed in other articles. For now, it is important that you remember:

(1) To factor means to re-write as multiplication, and

(2) Factoring is important because it is used to reduce algebraic fractions and to solve equations.

Algebra - Masterminding Maths in the Easiest Way

When a child first steps into his kindergarten school room, he looks at the world with rose colored glasses. Hardly does he realize what is waiting for the next twenty years of his educational life. He is introduced to his alphabets first and starts to play with his 'A B C D'. In his days of playschool, it is beyond his imagination, how his A, B, C and X Y Z can cause him spending a chain of sleepless nights in a row before his mathematics examination. Mathematics is one subject which ends up terrorizing some of us (better to be read as many) throughout our student life. It is in fact amusing to note how some researches show the percentage of mathematics freaks being elevated among the fairer sex. With so much mathematical troubles especially in a difficult and intricate field like algebra, most of us need guidance in mathematics beyond the reach of classroom teaching.

All those people who are stricken by continued euphoria due to the problematic combination of numeric's and alphabets, should opt for the specialized coaching classes held for educational assistance in mathematics. Algebra mainly deals with the study of the relation between quantity and construction of variables by basic addition, subtraction, multiplication and division at its root frameworks. At a little more advanced stage, it also demands the factorization and roots of different numbers, polynomials and variables in question. The elementary classified segments in algebra are pre-algebra, linear-algebra, elementary algebra, abstract algebra and universal algebra.

The crucial fields of algebra which students require to specialize in are basic equations, polynomials, a single or a set of variables and fundamental arithmetic. The usually required for concepts are fundamental theorem, the quadratic, linear, cubic, polynomial, quintic and quadratic equation. Tutors for the most sought after topics of algebra are very easily found these days as competent professors and teachers and even people in other respectable positions are taking up tutoring as their part time earning. You can not only find tutors online, but also avail the algebra tuitions given out over the net. Even nowadays so many recorded tutorial CD's are also available in the market to help you learning algebra. So if you want to be an adept in Algebra it's time to improve your knowledge, this could be a private tutor or an online tutorial both can play a significant role to enhance your knowledge-base.