About This Course

Before beginning this course on factorization, it is important to make sure that you already understand some basic skills in arithmetic and algebra. These will form the foundation for everything that follows. If you are confident with the topics listed below, then you are ready to move forward. If not, you may want to revise them briefly before starting.

First, you should be comfortable with arithmetic skills. This includes multiplying and dividing whole numbers, fractions, and decimals. You should also know how to find prime factors of a number, for example writing $18=2\times 3218\; =\; 2\; \backslash times\; 3^2$. Another important arithmetic skill is finding the greatest common factor (GCF) and the lowest common multiple (LCM). These ideas will help you when you are identifying common factors in algebraic expressions. You should also be confident when working with positive and negative numbers, since factorization often involves sign changes.

Second, you need a basic understanding of algebra. You should be able to identify terms, coefficients, and variables. For instance, in $5x2y5x^2y$, the coefficient is 5, the variables are $xx$ and $yy$, and the degree is 3. You should already know how to expand simple brackets, such as $(x+3)(x+2)=x2+5x+6(x+3)(x+2)\; =\; x^2\; +\; 5x\; +\; 6$. You should also know how to collect like terms, for example simplifying $3x+7x3x\; +\; 7x$ to $10x10x$. These are the kinds of skills that make factorization easier to understand.

Third, you should understand indices (powers). This means knowing that $x2=x\times xx^2\; =\; x\; \backslash times\; x$, $x3=x\times x\times xx^3\; =\; x\; \backslash times\; x\; \backslash times\; x$, and so on. You should also recall the index laws, such as $x2\cdot x3=x5x^2\; \backslash cdot\; x^3\; =\; x^5$ and $x4x2=x2\backslash frac\{x^4\}\{x^2\}\; =\; x^2$. Indices are part of many algebraic expressions, so these rules will be used often in factorization.

Fourth, you should be able to solve simple linear equations, such as $2x+5=112x\; +\; 5\; =\; 11$. Understanding that equations are balanced and that whatever is done to one side must also be done to the other side is essential.

Finally, since some applications of factorization involve geometry, you should know the area of a rectangle and be able to connect it to algebra. For example, if the area is given as $x2+5x+6x^2\; +\; 5x\; +\; 6$, factorization will help you find the possible length and width.

If you can do all of these comfortably, you are ready to start mastering factorization.