ʕ•ᴥ•ʔ Easily Learn to Solve Quadratic Equations by Factoring

ʕ•ᴥ•ʔ Easily Learn to Solve Quadratic Equations by Factoring


Solve the equation by factoring. Now,
for those of you that forget how to do factoring, now is a good time to go back
to an earlier chapter called “factoring,” where I taught all the techniques and
tricks to do factoring. Cool. Back to this question here. So, to factor this
trinomial, the first thing you got to ask yourself is, “well, between the numbers
here, is there a common factor?” Well all three numbers are even numbers, so that
means they must be divisible by 2, so let’s factor out 2. Okay? And what do we
have left inside the bracket? Well for the first term, 2x squared, factor out the 2,
what do we have left? Just x squared right? Now, for the second term, negative
12x. Now what do we factor out? We factor out 2, so you got to divide this by 2. So
what do we have left? Negative 12 divided by 2, we have negative 6x So we have
negative 6x left inside the bracket. Now for the third term, the constant term,
positive 10, what do we factor out again? We factored out 2, so divide by 2, so we
have 5 left inside the bracket. Positive 5. Okay? Cool. Now, how do we factor this
trinomial inside the bracket? Well, do you remember a very powerful technique called
cross multiply, then check? Right? So let’s use that technique to factor this
trinomial, okay? So, look at the leading term x squared, we can break it apart as x
times x right? Now, look at the constant term, positive
5. Well, positive 5 can be positive times positive 1. Right? Because positive 5
times positive 1 is positive 5. But is zero another option? Yes. Negative 5 times
negative 1 is also positive 5. Because negative times negative, we get positive.
And see, the negative is the better choice here because check this out, the middle
term we are looking for is negative. Right? So, negative should be the better
choice here. Okay? So now let’s do cross-multiply, then check. So,
cross-multiply this way, negative 5 times x, we get negative 5. Cross-multiply
this way, x times negative 1, we get negative x. And combine everything
here what do we have? After cross-multiply we got to what? Check, right? So that’s
why the technique is called cross-multiply, then check. Okay? So, now
we have to check here, so combine everything on the bottom line here, we
have negative 6x. Now you got to ask yourself, “Does this match the middle
term?” Yes, negative 6x. That means we are good. See? That means our factoring
is correct. So now, two factors. First factor is x minus 5. Second factor
is right here, x minus 1. Now the rest is easy. To solve this equation, wow
super easy. Ask yourself, guys. . . look at the first bracket here. What x value
will make this whole thing equal to zero? Well, would you say x must be 5
because 5 minus 5 is zero. Right? Now what x value will make this whole thing equal
to zero? X must be what? One right? Because 1 minus
1 is zero. And guess what? That’s the answer. Right? So the solution for this
quadratic equation is x equals 5 and x equals 1. So we have two solutions
for x.

37 thoughts on “ʕ•ᴥ•ʔ Easily Learn to Solve Quadratic Equations by Factoring

  • November 13, 2016 at 2:13 am
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    Man I wish this guy is my teacher I learnt a lot

    Reply
  • November 23, 2016 at 9:13 pm
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    your good I my that dumb cause my class is in the lowest tier

    Reply
  • December 2, 2016 at 6:13 pm
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    nice…

    Reply
  • December 10, 2016 at 1:21 pm
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    Yes ,the time that is taken to explain what ever it is there solving makes all the difference.

    Reply
  • December 11, 2016 at 10:37 pm
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    I like how he says

    Reply
  • December 11, 2016 at 10:38 pm
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    vry nice jawline
    vry asian 1:15 on my fav part

    Reply
  • December 14, 2016 at 6:35 pm
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    whats his name?!!! aa he is so cute! xx hehehehe

    Reply
  • December 14, 2016 at 6:36 pm
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    i like how he says: " cross-multiply" so cute

    Reply
  • February 22, 2017 at 3:29 am
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    What if the polynomial equals anything that is not 0

    Reply
  • March 8, 2017 at 8:29 am
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    i used to do this with calculator cuz everytime i read the textbook about this, i'd get confused. but now i finally understand. Thank you.

    Reply
  • March 19, 2017 at 3:09 pm
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    So I'm in advanced 8th grade classes and I know how to factor the polynomials. But, I am quite unsure of how to solve polynomial word problems, I get quite confused. Is there a site and/or video of yours that I can use to understand said problems?

    Reply
  • March 25, 2017 at 2:51 pm
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    ʕ•ᴥ•ʔ

    Reply
  • April 1, 2017 at 12:48 am
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    What about for 4x^2 – 12x + 9 = 0 ??

    Reply
  • April 26, 2017 at 9:45 pm
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    You are one of the best teachers ever, im now starting to get to grasps with this subject thanks to you. Greetings from England

    Reply
  • May 30, 2017 at 6:53 am
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    Thanks study pug…😃😃😃😃😃😃

    Reply
  • June 11, 2017 at 5:21 pm
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    great video has helped me so much thank you

    Reply
  • August 3, 2017 at 5:50 am
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    Studypug makes math fun to learn

    Reply
  • September 16, 2017 at 7:15 pm
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    can you please make 'Solve Quadratic Equations by completing the square'

    Reply
  • October 24, 2017 at 2:19 pm
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    I just entered College Algebra and this is more helpful than my professors notes, lectures, and textbook. Wow! Keep up the great work!

    Reply
  • November 23, 2017 at 12:22 pm
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    I never got how to factories but u helped me thank you!!!!!:)))))

    Reply
  • January 1, 2018 at 9:15 am
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    The gentlemen in the video is awesome!  I wish all college professors can teach like him.

    Reply
  • January 25, 2018 at 11:28 pm
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    Lol I love how enthusiastic he is when teaching maths; I guess someone has to be!😂😣..

    Reply
  • February 20, 2018 at 8:50 pm
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    T-Minus 40 minutes before my math exam. Commence the studying.

    Reply
  • May 14, 2018 at 11:32 pm
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    Thank you so so so much, I’m really hopeless when it comes to math but I really do try! You made it so much easier, I was having a panic attack, I couldn’t find people who knew how to explain it in a way that I would get it but then I found you, thank you so so much but now I do have confidence that I will pass thank you so much 😊

    Reply
  • May 25, 2018 at 11:57 pm
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    This is explained so well thank you so much

    Reply
  • May 31, 2018 at 9:46 pm
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    I love the board!!!!

    Reply
  • September 6, 2018 at 12:12 pm
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    This lesson had been my problem the entire week and all it takes for me to understand it is this video and a great teacher

    Reply
  • October 12, 2018 at 12:24 pm
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    so good man
    u the best
    i subed
    thz

    Reply
  • November 6, 2018 at 4:23 am
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    Bless you! Thank you so much this is so clear I wonder how my teacher was explaining this to make me confused!

    Reply
  • January 1, 2019 at 5:53 pm
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    good vid m8

    Reply
  • January 9, 2019 at 5:51 pm
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    Your very helpful, and explain your subject great

    Reply
  • March 20, 2019 at 5:28 pm
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    will i will have an exam tomorrow and iam counting on you all the time thank you very much

    Reply
  • April 4, 2019 at 10:09 pm
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    Can you do m square +21m+100 please

    Reply
  • April 16, 2019 at 1:55 pm
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    Quadratic inequalities can you make a video for it

    Reply
  • May 13, 2019 at 12:11 pm
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    Seems like a nice chap but I don't think his explanation was very good.

    Reply
  • July 8, 2019 at 3:38 pm
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    I understand a lot thank you very much and btw you're so hot XD

    Reply

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