Factor Polynomials - Understand In 10 min
TLDRThis video script offers essential tips on factoring polynomials, crucial for success in algebra and related math courses. It introduces four common scenarios for factoring, emphasizing the importance of starting with the greatest common factor (GCF). For trinomials without a GCF, two cases are discussed: 'case one' with a leading coefficient of 1, and 'case two' with a different coefficient, using strategies like the 'double smiley face' technique. The script also touches on special factoring rules, such as the difference of squares. The instructor suggests additional resources for those seeking more in-depth instruction.
Takeaways
- π The video aims to provide tips on factoring polynomials, covering the most common situations encountered in algebra and algebra 2.
- π The presenter emphasizes that understanding multiplication of polynomials is crucial for successful factoring, suggesting that without this knowledge, passing algebra could be difficult.
- π The video outlines four scenarios that cover most polynomial factoring situations, suggesting a structured approach to tackling different types of polynomials.
- π The first scenario is identifying and factoring out the Greatest Common Factor (GCF), which is the starting point for any polynomial factoring.
- π The script provides a brief tutorial on how to factor out the GCF, illustrating with examples and suggesting that viewers check additional resources for a deeper understanding.
- π After checking for a GCF, the next step is to look for trinomials, specifically distinguishing between 'case one' trinomials with a leading coefficient of 1 and 'case two' trinomials with a different leading coefficient.
- π The video introduces a method for factoring 'case one' trinomials by finding pairs of factors of the constant term that add up to the middle term's coefficient.
- π For 'case two' trinomials, the presenter introduces the 'double smiley face' technique, which involves factoring the leading coefficient and finding factors of the constant term that lead to the correct middle term when combined.
- π Special factoring scenarios are mentioned as the last resort if neither a GCF nor a trinomial situation applies, with the 'difference of squares' being highlighted as a key special factoring rule.
- π The presenter wraps up by stating that the video provides a foundation but not a complete education on factoring, encouraging viewers to seek further instruction through additional videos or math courses.
- π The video concludes with a call to action for viewers to subscribe, hit the notification bell, like the video, and leave comments for feedback, indicating the presenter's engagement with the audience.
Q & A
What is the purpose of the video?
-The purpose of the video is to provide powerful tips on how to factor polynomials commonly encountered in algebra, algebra 2, or college-level math courses.
Why is it important to know how to multiply polynomials before learning to factor them?
-It's important to know how to multiply polynomials because understanding the multiplication process helps in reversing the process, which is essentially what factoring is.
What is the first step you should take when attempting to factor a polynomial?
-The first step is to check if you can factor out a Greatest Common Factor (GCF) from the polynomial.
What should you do if there is no Greatest Common Factor in a polynomial?
-If there is no GCF, you should then check if the polynomial is a trinomial and determine its type.
How do you factor a trinomial where the leading coefficient is 1?
-For a trinomial with a leading coefficient of 1, you list all pairs of factors of the constant term and find the pair that adds up to the middle coefficient.
What is the double smiley face technique?
-The double smiley face technique involves multiplying certain pairs of factors to find the correct factorization of a trinomial where the leading coefficient is not 1.
What should you check if a polynomial is neither a GCF case nor a trinomial?
-You should check if the polynomial fits any special factoring scenarios, such as the difference of squares.
What is the difference of squares formula?
-The difference of squares formula is a^2 - b^2 = (a + b)(a - b).
What are the four main scenarios covered for factoring polynomials in this video?
-The four main scenarios are: factoring out the GCF, factoring a trinomial with a leading coefficient of 1, factoring a trinomial with a leading coefficient other than 1, and using special factoring rules like the difference of squares.
What additional resources does the instructor suggest for those struggling with factoring polynomials?
-The instructor suggests watching more of his YouTube videos or enrolling in his math courses for more extensive instruction.
Outlines
π Introduction to Polynomial Factoring Techniques
This paragraph introduces the video's purpose, which is to provide powerful tips on factoring polynomials commonly encountered in algebra, algebra 2, or college math courses. The speaker emphasizes that while the video will be helpful, additional resources such as other videos on the YouTube channel or math courses are available for those who need more extensive instruction. The paragraph sets the stage for four different factoring scenarios that will be covered, starting with the importance of knowing how to multiply polynomials before attempting to factor them. It also highlights the necessity of understanding factoring for success in algebra-related classes.
π Identifying Polynomial Factoring Scenarios
The second paragraph delves into the process of identifying the different scenarios one might encounter when factoring polynomials. It outlines a systematic approach starting with looking for the Greatest Common Factor (GCF), then moving on to trinomials, and finally considering special factoring scenarios. The speaker introduces 'case one' and 'case two' trinomials, explaining that 'case one' involves a leading coefficient of 1, while 'case two' involves a different leading coefficient. The paragraph also introduces the concept of special factoring rules, such as the difference of two squares, and encourages viewers to check out additional resources for a deeper understanding.
π Techniques for Factoring Trinomials and Special Cases
This paragraph focuses on the techniques for factoring trinomials, specifically 'case one' and 'case two', and special factoring scenarios. For 'case one' trinomials, the method involves finding pairs of factors of the constant term that add up to the linear coefficient. For 'case two', the 'double smiley face' technique is introduced, which involves factoring out the greatest common factor from the quadratic term and then finding factors of the constant term that, when combined with the linear term, yield the middle term. The paragraph also revisits the special factoring rule of the difference of two squares as an example of a special scenario. The speaker wraps up by emphasizing the importance of practice and provides a final reminder about additional resources available for those who need more help.
Mindmap
Keywords
π‘Factoring Polynomials
π‘Greatest Common Factor (GCF)
π‘Trinomial
π‘Case One
π‘Case Two
π‘Special Factoring Scenarios
π‘Difference of Squares
π‘FOIL Method
π‘Distributive Property
π‘Algebra
π‘Math Courses
Highlights
The video aims to provide powerful tips on factoring polynomials, covering the most common situations in algebra, algebra 2, and college math.
The presenter emphasizes the importance of understanding polynomial multiplication as a prerequisite for successful factoring.
The video offers a structured approach to factoring polynomials, starting with identifying the greatest common factor (GCF).
A detailed explanation of how to factor out the GCF from a polynomial is provided, with an example to illustrate the process.
The presenter introduces four different scenarios for factoring polynomials, which cover the majority of situations encountered in algebra classes.
A special focus is placed on trinomials, with two specific cases (Case 1 and Case 2) discussed in detail for factoring.
Case 1 trinomials, with a leading coefficient of 1, are factored by finding pairs of factors that add up to the middle term's coefficient.
Case 2 trinomials, with a leading coefficient other than 1, are approached using the 'double smiley face' technique to find the correct factors.
The video explains the process of identifying and applying special factoring rules, such as the difference of squares, to polynomials.
The presenter provides a method to verify factored polynomials by multiplying the factors to ensure they match the original polynomial.
Additional resources, including more videos and math courses, are suggested for those who need extensive instruction on factoring polynomials.
The video encourages practice as a key to mastering polynomial factoring, especially for those struggling with the concept.
The importance of being able to factor polynomials is stressed as a necessity for passing algebra and related math classes.
The presenter offers a mental organization strategy for approaching polynomial factoring, starting with GCF, then trinomials, and finally special scenarios.
A call to action is made for viewers to subscribe to the presenter's YouTube channel and engage with the content through likes and comments.
The video concludes with a reminder of the importance of understanding polynomial factoring and the availability of further help through the presenter's courses.
Transcripts
okay how to factor polynomials so the
purpose of this video is I'm going to
just try to give you some powerful tips
on how to factor the most polynomial
situations you're gonna come across in
in algebra or algebra 2 or college
chapter but of course you might be that
involves factoring polynomials these are
gonna be the most common situations now
I just want to tell you right up front
that this is you know you're not gonna
be able to if you're lost in this
subject if you will this is going to
help you out but it's not gonna be
enough so I have additional videos on my
youtube channel but if you really need
extensive instruction and I kind of
suggest that's the case for a lot of
people who are struggling they might
want to check out my math courses I'll
leave a link in a description of this
video if you're interested in learning
more from me and kind of in a formal
manner but with that being said let's
get into these four different type of
problems that will cover the majority of
polynomial situations that you may face
in any one of these particular or math
classes that you might be taking now
before you can factor a polynomial you
have to make sure that you can multiply
polynomials so if you don't know how to
multiply two polynomials together like
using the foil method or the
distributive property then you're then
you're gonna really struggle factoring
polynomials and I'll say additionally if
you can't factor polynomials then you're
going to struggle the department's going
to be impossible for you to pass your
algebra class or whatever other math
class you might be doing if it involves
algebra so this is an absolutely
necessary
topic to to learn in math okay so I've
got four different situations here and
let's get into it and if you understand
these four scenarios then you're gonna
be able to really handle most polynomial
factoring problems that you encounter in
algebra alright so the first is this
problem and this represents the GCF
technique now the GCF is a greatest
common factor you always always start
when you're looking at a polynomial to
see if you can factor out a greatest
common
factor okay now here you can so each one
of these proms that I have done your are
fact able so if you want to pause the
video just factor them real quick then
out of you know then see my answers and
that's kind of a good little pop quiz
for you and these are pretty simple
proms some I wouldn't get in a silly too
overly confident if you can handle these
but that's a it's a good indication that
you know what you're doing anyways let's
get into this the greatest common factor
is your the first place you always start
when you see up on the walls seemed he
could factor out a greatest common
factor now here what that is is the
greatest well it's exactly what the name
says it's the greatest common factor so
what's common amongst these two terms
here in terms of a number well it's four
okay then they have the highest power of
X this is X cubed this is x squared but
they're old but they only share an x
squared there's there is in common so
you would factor out an x squared like
so and that would leave you with an X
right here minus 2 okay now if you
weren't sure if this was the correct
answer you can multiply these together
and you can see you'd get back to this
answer okay and so this right here for x
squared is the greatest common factor
okay that is the greatest common factor
now again in a short period of time I'm
not going to be able to teach you
everything you need to know about the
greatest common factor so you should be
somewhat familiar with how to do this
but when it comes to factoring
polynomials is this is the number one
place you want to start okay so if you
don't know how to if you're not
comfortable with what factored out the
greatest common factor I have videos on
my youtube channel I go into it plus you
know you might need more extensive
instruction so you might want to check
out one of my courses just check out the
link below okay so that's the first
scenario okay now the second scenario is
this if you can't factor out a greatest
common factor okay let's say you're
looking at a polynomial and there is no
greatest common factor well that doesn't
mean that you're done
okay what you may have is one of these 3
remaining situations okay so let's just
kind of talk about these here so this is
what we call a trinomial there's three
terms but there's no greatest common
factor this is also a trinomial there's
three terms but there's no greatest
common factor and the difference between
these two trinomials is this one is just
a 1 x squared there's just a 1 in front
of it and then this has a number other
than 1 so here in this example this is 2
okay so what we have here are trinomials
trinomials so this is where you want to
look for next ok so you checked out
greatest common factors and you're gonna
see if there's any trinomials so the
last problem here you might encounter is
a special factoring scenario okay so
just we'll put the word here special so
these four scenarios here four
situations will cover the majority of
your factoring scenarios ok now I'm
gonna get into these problems these last
three problems here in a second but I
just wanted to just lay out the kind of
like you're a mental organization in
terms of hey I got a factor a polynomial
I always start with the GCF if I'm
dealing with a trinomial what type is it
I like to refer to this as a case one
because there's a wonder front of it and
then anything else is what we call like
say a case two
all right and if it's if you don't have
a case one or case two then see if
there's any special factoring rules that
uh that could apply to the polynomial
okay so let's get into this so very
briefly the case one is a trinomial
where there's just a 1 in front of the
leading it so the 1 is the leading
coefficient okay so when you write it in
standard form so if you look here the
easiest way to factor a case 1 if if
they are factorable okay let me just do
it this way is look at this last number
okay
that's negative 6 now one way I kind of
like to start students off
a factor in case once is to write out
all the factors of a negative six so
here's how you do okay so negative six
you can write as one times six a
negative one times six right will give
you a negative six 1 times a negative
six will give you a negative six okay
two times three negative two times three
and two times the negative three so
these are all the different ways you can
write the factors of negative six right
all these numbers these different
combinations will when you can multiply
these these pairs together we'll get you
a negative six now if you add up each
one of these pairs which what do you get
here you get a positive five right
negative one plus six is a positive 5
one plus negative 6 is negative five
this right here is a one and this is a
negative one right so when you add all
these pairs together so what you want to
do is to see if you have a pair any
pairs of factors that add up to this
Center number okay so this is a one x
squared this is a positive one so which
one of these pairs adds up to a positive
one it's these pairs right negative two
plus three gives you a positive one and
these are the answers these are the
factors so you could write this
trinomial you can factor it this way
okay you're always going to have two
binomials so it's going to be X minus
two
okay one of those answers and X plus
three right there so these are the
factors to that trinomial as simple as
that
okay of course you need to practice this
now if you couldn't find any pairs of
factors here that add up to that Center
number then a factor and then the
polynomials unfactored
so this one one in this case two now the
case two you could do you can do this in
a similar manner but there's some
additional steps but I'm gonna give you
another technique you can use to try to
factor a case to let me write this a
little better I kind of call it the
we'll smiley face so the first thing is
we have 2x squared so we want to write
the factors of 2x squared doesn't
there's only one way to factor that that
would be a 2x and X right so if I
multiply 2x and X together I get a 2x
squared there's no other way I could
write that now what we're trying to do
here is play a little game to try to get
back to this Center number now the way
we have to do that is write the factors
of negative 5 in this position right
here you'll see how this comes together
here in a second so negative 5 is what 1
times negative 5 or negative 5 times 1
so I'm gonna put this negative 5 right
there and I'm gonna put a 1 right there
okay now if what if what I'm gonna show
you doesn't work I can just kind of
maneuver these combinations around
because I'm trying to get back to the
center number now I told you I was gonna
use something called a double smiley
face technique so what that is is you
take this number here and you're
multiply it by this okay and that's one
smile when you face if you will and then
we do this times this so you can see we
have two smiley faces let me draw this
the other one a little bit bigger okay
so we have one X right 1 times X is X or
1 times X is 1 X positive 1 X and then I
have 2 x times a negative 5 that's
negative 10 X now if I add these two
guys together you're looking to see
which combination gets back to the
center term so if you see here a 1 X a
positive 1 X plus a negative 10 X gives
me a negative 9 X so this these factors
right here are correct okay because of
that and if you wanted to you can just
multiply all this out to verify that in
fact you have the correct factors okay
so this is the double smiley face now
you could do this problem and they're
similar fashion as I did this first case
one problem but there's some additional
steps so I really like to kind of the
double smiley face technique for this
case two polynomials and for case one
this this technique I
showed you here is just really
straightforward okay so I would suggest
using that as well okay so now you have
three things we have three things behind
us right we have the greatest common
factor we always look there first then
if we're dealing with trinomials what
type and if we don't have any trinomials
we don't have any greatest common factor
that doesn't mean that you're done you
may have a special factoring scenario so
if you look here this last problem
there's no GCF it's not a trinomial so
what do you do well in this case you
just need to know that special factoring
rules probably one of the most important
is a squared minus B squared owes me
write this this way here a squared minus
B squared is equal to a plus B times a
minus B it's called the difference of
two squares it's used extensively okay
when we're talking about factoring so
here the way I would factor this I would
just simply need to know this rule this
is a special factoring role so this is
going to be X plus 3 times X minus 3 ok
all right then a little bit better so
this is how this factors here because I
know the special factor in a rule now
again I'm gonna wrap up this video here
no way I could I fit in what takes your
teacher a couple weeks to teach you at
least the factoring is it's covered you
know and over and over a multiple math
courses so this is this is a lot of you
know skills that kind of build up no way
I should you expect to just watch this
video be like a total expert but if you
have a clue about factoring and you know
how to multiply and you're like I just
kind of struggling are a little bit
confused then I think this video would
definitely should have helped you out
right because you're always start here
you'll always start with the GCF then
look to see if you have any of these
scenarios and then if you don't just
make sure you don't have any special
scenarios if you follow this you're
going to be good to go in most factoring
situations but again if you need more
help you want to go ahead and check out
some additional videos I have on my
youtube channel so please consider
subscribing and if you do hit that Bell
notification and if you liked this video
hey you know give me a thumbs up I
appreciate that
and leave me comments it's um it's one
of the things that I tried to read it I
do get a lot of comments on my videos
which I'm grateful for but it gives me
feedback on on videos that I future
videos I can make that are going to help
help you out again
you know if you like my teachings down
you understand you know you know how I
teach and you need extensive help in
math then you might want to consider
check it out some of my math courses and
I'll leave a link in a description in
the video if you're interested there but
other than that I appreciate your time
and have a great day
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