How To Factor Polynomials

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Factoring polynomials is a fundamental skill for all math students. It is an important part of solving problems and expanding equations. Whether you are a high school student learning pre-calculus, or a college math major, understanding how to factor polynomials is a critical skill.

First, you must understand what a polynomial is. A polynomial is an algebraic expression composed of one or more terms that involve sums and/or difference of constants and variables raised to a certain power. For example, the polynomial 4x

^{2}+ 2x – 3 is composed of three terms. The first term is 4x^{2}, with an exponent value of 2. The second term is 2x, with an exponent of 1. The third and final term is -3, with an exponent of 0.To factor a polynomial, you need to break down the terms into multiple components. You can do this by using the following two methods:

Factor by Grouping: This technique involves grouping the polynomial terms into groups of two (or more) and then factoring out common elements. For example, you can factor the polynomial 4x

^{2}+ 2x – 3 by grouping the first two terms into one group and the third term in a separate group. Then you can factor out the common factor of 2 from the first group (2x), and the constant -3 from the second group. This simplifies the polynomial to (2x + 3)(2x – 1).Factor by Identifying Patterns: This technique involves looking for patterns in the polynomial that can be used to identify a common factor. For example, the polynomial 6x

^{2}+ 12x + 8 can be factored by identifying the pattern of a perfect trinomial (two consecutive numbers multiplied by each other). In this case, the perfect trinomial is 6x and 8. This means that 6x is the common factor in both terms, which can be factored out. This simplifies the polynomial to (6x)(x + 2).When factoring polynomials, it is a good idea to both use the two methods above. This will ensure that you factor out all of the common factors and leave the polynomial in the simplest form possible.

No matter your background in mathematics, understanding how to factor polynomials is a skill that can be acquired with a little practice. Once you understand the techniques described in this article, youâ€™ll be on your way to becoming a polynomial-factoring pro.