To begin to understand how to factor, take a look at how you can factor simple numbers. You can factor the number 64 for instance as follows: 1, 2, 4, 8, 16, 32, 64. Mathematicians divide numbers into two categories when factoring, prime and composite numbers. Prime numbers have only two factors: one of these is 1, and the other is the number itself. 1, 3, 7 and 11 are examples of prime numbers. Examles of composite numbers are: 4, 6, 8 and 10.
To factor algebraic expressions, find the terms' greatest common factor. You should find the greatest common factor of the coefficients (the numbers in front of the variables) first, and then move on to the variables. For example, you can factor "4x^3 + 8x^4 + 16x^5" as "4x^3(1 + 2x + 4x^2)" because 4 is the greatest common factor of 4, 8 and 16, and "x^3" is the greatest common factor of x^3, x^4 and x^5.
You can use the "FOIL" method to check your work after factoring. FOIL is a mnemonic device whose letters stand for "first, outside, inside, last." FOIL tells us the order in which you multiply your terms. To FOIL (2x-3) (4x+7), begin by multiplying the "first" terms, 2x and 4x, yielding a product of "8x^2." Then multiply the "outside" 2x and 7; "inside" -3 and 4x; and "last" -21. Your "FOILED" product should be:
8x^2 +14x - 12x - 21
Complete the necessary subtraction steps to receive the final product of:
8x^2 +2x - 21
There are four main steps to simplifying algebraic expressions. The first step involves multiplying factors to remove parentheses, and the second step multiplying exponents, if the are present, to remove them. In the third step, you add coefficients to combine like terms, and in the final step you combine constants. You would simplify the following expression "10x^2 + 14x - 4x^2 - 20x + 10" as "6x^2 - 6x + 10."