Polynomial Equations

What does factoring polynomials mean?

When a polynomial is written as the product of two or more polynomial equations, the polynomial has been factored. This allows a complicated polynomial to be broken up into easier, lower degree pieces; and it makes the equation easier to solve. One way to look at it is that factoring a polynomial is the opposite process from multiplying polynomials.

One of the most basic ways to factor a polynomial is similar to factoring a number. When a number is factored, the result will be the prime factors that multiply together to give the number (for example, 6 = 2 × 3 , or 12 = 2 × 2 × 3; see “Math Basics” to learn more about prime factors). With polynomials, this is often called “taking out a common factor”: If every term in a polynomial expression has several factors, and if every term has at least one factor that is the same, then that factor is called a common factor. If this is the case, then the common factor can be removed from every term and multiplied by the whole remaining expression.

For example, for the equation 2x2 + 8x, the first term has factors of 2 and x, while the second term has factors of 2, 4, and x. The common factors are 2 and x, making 2x the overall common factor. This makes the expression equal to 2x(x + 4). Thus, it is easy to see that when a polynomial is factored, it results in simpler polynomials that can be multiplied together to give the initial polynomial.


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