Problem Solving Made Easy (8th Grade) #7: How to Factor a Trinomial by Grouping?

Hello steemian friends! Today's post discusses the steps in "How to factor a trinomial by grouping? ". 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).

I admit, factoring this type of trinomial the easier way is no easy at all. With the way majority of my students respond to learning nowadays is a real battle to win! Though I am into this scenario for years, it still saddens me when no matter how much effort I've done, they just settle on low scores ( well I'm talking to my regular classes since students in my "Pilot Class" are fast learners which makes life a bit easier )

Every time we do have our LAC session (Learning Action Cell ), we teachers share the same old lament in common. Only a few of these young human can be seen exerting effort in learning the hard way. Mostly, they'll just learn in a moment then gone the next day. So instead of just having a quick recap of the last lesson, the need to reteach it is a must. And if you won't, I tell you, you can't stand to the way they make fun of their low scores. Nah! You shouldn't wear a pale heart or else take it seriously and you will die early!

In my case, instead of overly thinking whose fault is it, reflecting on the same old question " what have I done?" I just strive to enjoy the company of this new generation. Anyway, how to teach is not the question, but rather how to stay in this profession is the real challenge. So let's start!

What is factoring by grouping? - A brief review

(It is assumed that the reader knows already how to do factoring by grouping. )

Most often, factoring by grouping is used in polynomials with more than three terms. Though it is not always obvious which terms to group and sometimes several different groupings will work, using this method in factoring a quadratic trinomial is the best option.

Here, let's take this for example,

The above trinomial is actually written on the form where and are the numerical coefficients of the variable, and is the constant term. Since the value of is not equal to , factoring a quadratic trinomial of this type is one of the most complicated tasks as complained by my eighth graders.

Finding as its factors, involve quite a bit of trial and error. We need to list all the possible factor pair that would sum up to the middle term. Thus, factoring by grouping would help to avoid doing those stuff.

How to factor a trinomial by grouping?

To successfully use this method, one should recall how to remove a common monomial factor as it is very essential as we progress in grouping the terms with a common factor. It also important to emphasize that a variable is part of its term. Often time my students focused only on its numerical coefficient setting aside the variable which would lead to a wrong answer. Now here, let's just stick to the same trinomial as our example.

Here are the steps:

Let be factored completely.

• Step 1. Multiply the first and the last term.

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• Step 2. Find the factors of whose sum is the middle term .

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(note: Here enters the trial and error in locating the factors that would give the sum of the middle term. )

• Step 3. Rewrite the trinomial as four-term expression by replacing the middle term by the sum factor.

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• Step 4. Group terms with common factor

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• Step 5. Factor the groups using greatest common monomial factor.

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• Step 6. Factor out the common binomial and write the remaining factor as sum or difference of binomial.

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Note: 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!

Therefore,

So we're done!
Can you imagine listing all the possible factor pair that would sum up to the middle term considering that and has its own list of possible factors too? Nah! That would be a tedious and a long process my students won't give in.

Well, thank goodness, factoring by grouping helps them to avoid doing all those tiresome stuff. Though this method still utilizes some degree of trial and error, you might as well find it comfortable to use now that you know how it is done. Till next time.

Steem on!

References:
Factoring trinomial by grouping
Factoring in pairs
Worktext inMathematics: e - math8
Textbook in Intermediate Algebra II

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