{"id":8478,"date":"2020-12-22T03:43:30","date_gmt":"2020-12-21T22:13:30","guid":{"rendered":"https:\/\/cbselibrary.com\/?p=8478"},"modified":"2020-12-22T14:28:48","modified_gmt":"2020-12-22T08:58:48","slug":"review-factoring-polynomials","status":"publish","type":"post","link":"https:\/\/cbselibrary.com\/review-factoring-polynomials\/","title":{"rendered":"Review Factoring Polynomials"},"content":{"rendered":"
This lesson will review the process of factoring, which is used when solving \u00a0equations and simplifying rational expressions.<\/p>\n
To factor polynomial expressions, there are several approaches that can be used to simplify the process. While all of these approaches are not used for each problem, it is best to examine your expression for the possible existence of these situations. Ask yourself the following questions:<\/p>\n
Factor out the Greatest Common Factor (GCF) of the expression, if one exists. This will make it simpler to factor the remaining expression.<\/p>\n
Take care NOT to drop this GCF, as it is still part of the expression’s answer.<\/p>\n
<\/p>\n
If it does, is the expression a DIFFERENCE of PERFECT SQUARES?
\nIf so, you should be able to write the expression as a product of the sum and difference of the square roots of the terms.<\/p>\n
Sometimes, as in Example 2 below, it is best to write the terms in square notation so
\nyou can see what the terms will be in factored form. Be sure to use parentheses!<\/p>\n
This process is also called Factoring with DOTS (Difference of Two Squares).
\n<\/p>\n
If yes, then the expression may factor into the product of two binomials. One way to solve this type of problem is to use trial and error, keeping certain “hints” in mind.<\/p>\n
Hints:
\nWith the trinomial arranged in proper order (highest to lowest powers):<\/p>\n
For the examples below, use the hint above for factoring when the leading coefficient is 1, and the trial and error (guess and check) method when the leading coefficient is 2.<\/p>\n
Always check your work by multiplying the binomials to see if your center term matches the original problem.<\/p>\n
<\/p>\n
Consider what happens when a binomial is squared:<\/p>\n
where the center term is twice the \u00a0product of a and b.<\/p>\n
If you can recognize this pattern, it is very easy to factor a trinomial that is the perfect square of a binomial.<\/p>\n
<\/p>\n
If yes, then factor out the negative sign first, using the common factor method at the top of this page.
\nRemember, if the leading term has a coefficient of (- 1), and there are
\nNO other common terms, then the GCF is = -1.<\/p>\n
<\/p>\n","protected":false},"excerpt":{"rendered":"
Review Factoring Polynomials This lesson will review the process of factoring, which is used when solving \u00a0equations and simplifying rational expressions. To factor polynomial expressions, there are several approaches that can be used to simplify the process. While all of these approaches are not used for each problem, it is best to examine your expression … Read more<\/a><\/p>\n","protected":false},"author":8,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[5],"tags":[3078],"yoast_head":"\n