Algebra has become a “must have” a course in high school. However, as technology continues to advance and become algebra in which every person should have the control, the success rate of students is still low. There are several reasons for this, but one reason is that students do not become proficient in mathematics. In fact, students in mathematics complain loudly if the vocabulary and spelling tests given, saying, “is not English class!”Students do not realize that if you do not master the vocabulary, perform poorly on tests because they do not understand what the index tells you to. Instruction “factor …” is an excellent example of this problem.
As factoring?
In simple terms, the process of “factoring” or “factor” word means rewriting algebraic expressions in terms of multiplication. Factoring is the process used at all Algebra, but if you ask even the best students that the word “factor” is concerned, very few respond correctly.
Students understand the factorization of arithmetic. Ask students “factor 6″, write 6 = 2 x 3.Ask students to “12″ factor can lead to 12 = 2 x 6 or 12 = 3 x 4, and some students can continue factoring until 12 = 2 x 6 = 2 x 2 x 3 x 2 = 2 ^ 3. Students know to consider a product of primes.
However, by requiring algebra in the early years to factor the expression 2x + 2y You will receive a room full of blank stares. No transfer their knowledge of arithmetic “factors” word algebra. Algebra for students to master the language, we must give our students many examples of what we do and we need our students say and explain the definitions and properties and give examples ALOUD.
Initially, factoring in algebra depends strongly on the distributive property. Surprisingly, students seem to understand quickly and efficiently using the distributive property of factoring two complex terms. Looking 2x + 2y, students generally recognize common multiplier 2. Then they learn to use the distributive property to rewrite the multiplication. 2x + 2y = 2 (x + y).
Students have difficulty getting a little more than the term is more complicated and / or increase the number of words, but with some examples and practice, students can factor expressions such as 3a + 9AB – 15AC. Every action, after two and three a. Again, using the distributive property, 3a + expression 9AB – 15AC in 3a (1 + 3b – 5c) when rewritten as a multiplication.
Note: One of the best things about factoring is that it can easily be checked by multiplication to check that the result is the original expression.
Now we know what factoring, we must understand why the factors.
Why we need the factor?
There are two main uses of factoring: (1) the reduction of fractions, and (2) solve the equation.
Reduce fractions:
As with factoring, students learn how to reduce fractions in arithmetic. 14/12 = (2 x 6) / (2 x 7) = (2 / 2) (07/06) = 1 (7.6) = 7.6.
To transfer this knowledge often cause problems in algebra, but also in arithmetic, algebra to reduce fractions using factoring and the fact that x / x = 1.
Reduce (3a + 9AB) / (the 3rd ^ 2 + 15AB).
This fraction must be 3 a (1 + 3b) / 3a (a + 5b) = (3a/3a) ((a + 3b) / (a + 5b)) = 1 ((1 + 3 b) / ( a + 5b)) = (a + 3b) / (a + 5b).
Solve the equation:
Some algebraic equations can be solved (which means finding the values that make the equation right), starting with the movement of all terms to one side of the equal sign. This leaves a zero on the other side. Then, if possible, the algebraic expression is a factor.Second, the fact that if ab = 0 or a = 0 or b = 0, we find a solution.
Resolve: 3a ^ 2 =.
This equation becomes ^ 2 – 3a = 0. Then, factoring gives (a – 3) = 0. So either = 0 or (a – 3) = 0. This indicates that we have two values that make the original equation is true: 0 to 3.
