How to pull out the greatest common factor of polynomials

The key is that all the terms of the polynomial need to share the factor being taken out. Any factor that’s shared by all the terms is called a common factor, and the factor that consists of everything which is shared by all of them is known as the greatest common factor. Factoring is “un-distributing,” which means that we do the opposite of distributing and take out (or “factor out”) the same factor from each term of the polynomial (and divide each term by that factor to get “what’s left” once it’s taken out).

Factoring quadratic equations with coefficients

In this lesson we’ll look at methods for factoring quadratic equations with coefficients in front of the x^2 term (that are not 1 or 0). Factoring means you’re taking the parts of an expression and rewriting it as parts that are being multiplied together (the factors). Factoring a quadratic equation means we will write equations of the form ax^2+bx+c into the form (px+r)(qx+s), where a, b, c, p, q, and s are all real numbers and a≠1,0.

Factoring out the greatest common factor from trinomials

The key to factoring is that every term in the trinomial needs to share the factor being taken out. Any factor that’s shared by all the terms is called a common factor, and the factor that consists of everything which is shared by all of them is known as the greatest common factor.

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