How to Factor in Algebra 2

Algebra 2 requires students to factor equations. Factoring is multiplication in reverse. Instead of combining like terms to create a shorter equation, you pull out like terms to create a longer equation. These like numbers are known as factors. Factoring can be done in different ways, depending on the problem, but the basics are simple to learn with a little practice. Here are the most common methods of factoring.

Instructions

1. Find the highest common factor in the equation. This is a number that can be evenly divided into each term of the equation. For example, 2 is a common factor of "6y - 8" because there is no larger number that can evenly be divided into 6 or 8.

2. Divide each term by the common factor, and place the common factor in parenthesis by each term. Using the same problem of "6y - 8" the equation would now read "2(3y) - 2(4)".

3. Follow the rule a(b + c) = ab + ac. This simply means that you can write a common factor once and put the rest of the equation in parenthesis instead of writing the common factor before each term in the equation. Since 2 is our common factor, place it outside the parenthesis and the other terms inside.
   This gives you 2(3y - 4). All you have done is divide 6y - 8 by 2 and written the answer in parenthesis. If you multiply (3y - 4) by 2, you'll get the original equation of 6y - 8.

4. Another type of factoring is with exponents. Check to see if both numbers have even square roots before factoring. If they do, such as the equation x^2 - 4^2 (the ^2 sign simply means that x and 4 are being raised to the second power), you can use the following formula: a^2 - b^2 = (a + b)(a - b).
   This says that your "a" term--in this case, "x"--is first added to your "b" term which is 4 in the equation x^2 - 4^2. That would be written as (x + 4). Then the "a" and "b" terms are subtracted, "(x - 4)". Finally, those two terms are multiplied together. To write this out, you would put "(x + 4) (x - 4)".

5. Include a letter variable such as "x" in the common factor, if possible. "2x" is the common factor of "4x + 6x" and could be written as " 2x (2 + 3)". All terms must have the same letter in them for the letter to be a common factor.

6. When you have longer equations, rearrange the equations so you can find the common factor of two or more sets of numbers. For example, "4x^2 - 3x + 20x -15" can be written as "4x^2 + 20x - 3x - 15". Then you can find the common factor of "4x^2 + 20x" and a separate common factor for "-3x - 15". Don't forget to include the negative sign with "-3". The answer to this equation would be "4x (x + 5) - 3 (x + 5)".

References

• Factoring in Algebra 2