Problem Solving Made Easy (8th Grade) #6: How to Factor Polynomial ...

_{How to Factor Polynomial by Removing the Greatest Common Monomial Factor?}

"Solving math problem the easier way is intended to help students discover that learning math is easy. Be inspired and motivated with the hope it can sway them from having neutral opinions about math to liking it."

Hello steemian friends! Today's post discusses the steps in "How to Factor Polynomial by Removing the Greatest Common Monomial Factor ". Again, I made it sure that the language used in the presentation is user-friendly in the sense that it is easily understood by a reader who has at least an 8th-grade education (age 13-14).

The department of education in my country has been looking for a solution on how students improved their liking on Math subject. Per observation, most of the students nowadays are poor in analytical thinking or they just don't want to think hard anymore. So, after the long days of training on "Critical Content" or least learn competencies, I am now set to find ways on how to teach the topic the easiest way.

Factoring Polynomials - A brief review

Factoring a polynomial is the opposite process of finding its product. If a polynomial is the product of other polynomials, then each of the latter polynomials is called a factor of the original one.

Today's post talks about the simplest type of factoring which involves a polynomial that can be written as the product of a monomial and another polynomial. The technique used here is based on the distributive property, a(b + c) = ab + ac, in the reverse direction. In Illustration we have,

To completely factor a polynomial, make sure each of its factors is prime. In here, we are to find the GCF and the other factor that when multiplied it will bring us back to the original polynomial expression. In the illustration above, 4x is the GCF while (x - 3) is the factor of 4x² - 12x. Let's see if when multiplied it will give us the original polynomial. Here,

So confirmed! It resulted back to the original polynomial expression.

How to Factor Polynomial by Removing the Greatest Common Monomial Factor?

Removing a common factor is the first step in factoring a polynomial completely. The common factor having the greatest numerical factor and with variables having the least degree is what we called the " greatest common factor (GCF)" of the polynomial. Below are the steps in finding the GCF of a polynomial and how to factor it completely.

Here are the steps:

Let be the polynomial to be factored completely.

Step 1. Find the greatest factor of the numerical coefficients.

Step 2. Find the variable with the least exponent that appears in each term of the polynomial

Step 3. Multiply the GCF of the numerical coefficient and the GCF of the variable to find the GCF of the polynomial.

Step 4. To completely factor the given polynomial, divide the polynomial by its GCF and the resulting quotient is the other factor.

Therefore,

( Note to ponder ) :

When we factor, nothing "disappears". We just rearranged things. Simply dividing out of every term and moving it to be in front of the parentheses. Alright!

Application:,

Now to check your understanding you may try this,

Factor completely the following polynomial.

You may follow the above steps. I just hope it will help. Till next time.

Steem on!

References:
Simple factoring
GCF
Worktext in Mathematics: e - math8

Images are all mine.

Problem Solving Made Easy (8th Grade) #6: How to Factor Polynomial by Removing the Greatest Common Monomial Factor ?