1. Home
  2. Elementary algebra
  3. Factoring
  4. Factor quadratic trinomials with

7.3 Factor quadratic trinomials with leading coefficient other than

<< Chapter < Page
  Elementary algebra     Page 1 / 6
Chapter >> Page >
By the end of this section, you will be able to:
  • Recognize a preliminary strategy to factor polynomials completely
  • Factor trinomials of the form a x 2 + b x + c with a GCF
  • Factor trinomials using trial and error
  • Factor trinomials using the ‘ac’ method

Before you get started, take this readiness quiz.

  1. Find the GCF of 45 p 2 and 30 p 6 .
    If you missed this problem, review [link] .
  2. Multiply ( 3 y + 4 ) ( 2 y + 5 ) .
    If you missed this problem, review [link] .
  3. Combine like terms 12 x 2 + 3 x + 5 x + 9 .
    If you missed this problem, review [link] .

Recognize a preliminary strategy for factoring

Let’s summarize where we are so far with factoring polynomials. In the first two sections of this chapter, we used three methods of factoring: factoring the GCF, factoring by grouping, and factoring a trinomial by “undoing” FOIL. More methods will follow as you continue in this chapter, as well as later in your studies of algebra.

How will you know when to use each factoring method? As you learn more methods of factoring, how will you know when to apply each method and not get them confused? It will help to organize the factoring methods into a strategy that can guide you to use the correct method.

As you start to factor a polynomial, always ask first, “Is there a greatest common factor?” If there is, factor it first.

The next thing to consider is the type of polynomial. How many terms does it have? Is it a binomial? A trinomial? Or does it have more than three terms?

If it is a trinomial where the leading coefficient is one, x 2 + b x + c , use the “undo FOIL” method.

If it has more than three terms, try the grouping method. This is the only method to use for polynomials of more than three terms.

Some polynomials cannot be factored. They are called “prime.”

Below we summarize the methods we have so far. These are detailed in Choose a strategy to factor polynomials completely .

This figure lists strategies for factoring polynomials. At the top of the figure is G C F, where factoring always starts. From there, the figure has three branches. The first is binomial, the second is trinomial with the form x ^ 2 + b x +c, and the third is “more than three terms”, which is labeled with grouping.

Choose a strategy to factor polynomials completely.

  1. Is there a greatest common factor?
    • Factor it out.
  2. Is the polynomial a binomial, trinomial, or are there more than three terms?
    • If it is a binomial, right now we have no method to factor it.
    • If it is a trinomial of the form x 2 + b x + c : Undo FOIL ( x ) ( x )
    • If it has more than three terms: Use the grouping method.
  3. Check by multiplying the factors.

Use the preliminary strategy to completely factor a polynomial. A polynomial is factored completely if, other than monomials, all of its factors are prime.

Identify the best method to use to factor each polynomial.

  1. ⓐ 6 y 2 − 72
  2. ⓑ r 2 − 10 r − 24
  3. ⓒ p 2 + 5 p + p q + 5 q

Solution

  1. ⓐ
    6 y 2 − 72 Is there a greatest common factor? Yes, 6. Factor out the 6. 6 ( y 2 − 12 ) Is it a binomial, trinomial, or are there Binomial, we have no method to factor more than 3 terms? binomials yet.

  2. ⓑ
    r 2 − 10 r − 24 Is there a greatest common factor? No, there is no common factor. Is it a binomial, trinomial, or are there Trinomial, with leading coefficient 1, so more than three terms? “undo” FOIL.

  3. ⓒ
    p 2 + 5 p + p q + 5 q Is there a greatest common factor? No, there is no common factor. Is it a binomial, trinomial, or are there More than three terms, so factor using more than three terms? grouping.
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Identify the best method to use to factor each polynomial:

  1. ⓐ 4 y 2 + 32
  2. ⓑ y 2 + 10 y + 21
  3. ⓒ y z + 2 y + 3 z + 6

ⓐ no method ⓑ undo using FOIL ⓒ factor with grouping

Got questions? Get instant answers now!

Questions & Answers

Discuss the differences between taste and flavor, including how other sensory inputs contribute to our  perception of flavor.
John Reply
taste refers to your understanding of the flavor . while flavor one The other hand is refers to sort of just a blend things.
Faith
While taste primarily relies on our taste buds, flavor involves a complex interplay between taste and aroma
Kamara
which drugs can we use for ulcers
Ummi Reply
omeprazole
Kamara
what
Renee
what is this
Renee
is a drug
Kamara
of anti-ulcer
Kamara
Omeprazole Cimetidine / Tagament For the complicated once ulcer - kit
Patrick
what is the function of lymphatic system
Nency Reply
Not really sure
Eli
to drain extracellular fluid all over the body.
asegid
The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include: 1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
asegid
to transport fluids fats proteins and lymphocytes to the blood stream as lymph
Adama
what is anatomy
Oyindarmola Reply
Anatomy is the identification and description of the structures of living things
Kamara
what's the difference between anatomy and physiology
Oyerinde Reply
Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.
AI-Robot
what is enzymes all about?
Mohammed Reply
Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems
Kamara
yes
Prince
how does the stomach protect itself from the damaging effects of HCl
Wulku Reply
little girl okay how does the stomach protect itself from the damaging effect of HCL
Wulku
it is because of the enzyme that the stomach produce that help the stomach from the damaging effect of HCL
Kamara
function of digestive system
Ali Reply
function of digestive
Ali
the diagram of the lungs
Adaeze Reply
what is the normal body temperature
Diya Reply
37 degrees selcius
Xolo
37°c
Stephanie
please why 37 degree selcius normal temperature
Mark
36.5
Simon
37°c
Iyogho
the normal temperature is 37°c or 98.6 °Fahrenheit is important for maintaining the homeostasis in the body the body regular this temperature through the process called thermoregulation which involves brain skin muscle and other organ working together to maintain stable internal temperature
Stephanie
37A c
Wulku
what is anaemia
Diya Reply
anaemia is the decrease in RBC count hemoglobin count and PVC count
Eniola
what is the pH of the vagina
Diya Reply
how does Lysin attack pathogens
Diya
acid
Mary
I information on anatomy position and digestive system and there enzyme
Elisha Reply
anatomy of the female external genitalia
Muhammad Reply
Organ Systems Of The Human Body (Continued) Organ Systems Of The Human Body (Continued)
Theophilus Reply
what's lochia albra
Kizito
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
<< Chapter < Page Page > Chapter >>
Practice Key Terms 1

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elementary algebra' conversation and receive update notifications?

Ask