Q:

How do you factor each polynomial completely?

A:

Factoring completely is an algebraic process that incorporates the three common factoring techniques: the greatest common factor, trinomials and the difference between two squares. These techniques by themselves often factor a polynomial into a single pattern, while factoring completely utilizes them together to simplify an expression as much as possible.

Keep Learning

Credit: Niko Guido E+ Getty Images

1. Factor the greatest common factor from the expression

In the example, 12x^4 - 3x^2 - 54, the greatest common factor is 3. Therefore, the 3 is removed from the initial equation, and the expression becomes 3(4x^4 - x^2 - 18). If there is no greatest common factor to be found, this step may be skipped.

2. Factor a trinomial

If there are more than two terms in an expressions, it may be factored into a trinomial. In the example, 3(4x^4 - x^2 - 18), the expression would become 3(4x^2 - 9)(x^2 + 2) when factored.

3. Factor a difference between two squares

Finally, in the example 3(4x^2 - 9)(x^2 + 2), (4x^2 - 9) may be factored as a difference between two squares. The expression then becomes 3(2x + 3)(2x- 3)(x^2 + 2) and is factored completely. Many equations may not be factored as a difference between two squares, in which case, this step may be skipped.

Sources:

Related Questions

• A: To factor the difference of two squares, break down the squares, and then factor them out to get the positive and negative solutions. The proper solution i... Full Answer >
Filed Under:
• A: To solve a polynomial inequality, first put a zero on one side of the inequality. Then, factor the inequality if it is factorable, although this attribute ... Full Answer >
Filed Under:
• A: A monomial, where “mono” means “one,” is a one-term polynomial. A binomial, with “bi” meaning “two,” is a polynomial with two terms. A polynomial with thre... Full Answer >
Filed Under:
• A: Writing a polynomial in standard form means putting the term with the highest exponent first. The other terms with lower exponents are written in descendin... Full Answer >
Filed Under:
PEOPLE SEARCH FOR