Factoring Quadratics... What If You Can't? (NancyPi)

Usually, a quadratic expression can be factored, but some cannot be, at least not with integer numbers. It's best to assume at the beginning that it can be factored, when you're trying to factor the expression. But if you've been working on a problem, and you've already gone through the steps explained in the introduction to factoring video, "Factoring Quadratics...How?", and it's not working, it might be the case that it cannot be factored (using integers).

1) Does the "trial and error" factoring method work for all QUADRATICS STARTING WITH X^2?
For example, say you need to factor the quadratic x^2 - 16x + 51. For the trial and error method, what you need to find are two numbers that multiply to give you the last number, positive 51, and that also add to give you the second number, -16. So first, list all the pairs of numbers that multiply to 51. Then, figure out which of those pairs also adds to negative 16. In this case, none of those pairs of numbers will add to negative 16, so this quadratic cannot be factored (over the integers). It turns out that sometimes the quadratic expression you’re given can't be factored, at least not in the way you're being asked to do in algebra, so you can just write "cannot be factored" as the answer.

2) What about for a quadratic expression that has a LARGER LEADING COEFFICIENT TERM like 2X^2 or 3X^2? Can the "magic X" method be used to factor any quadratic expression?

CAUTION: if your leading coefficient can be factored out from every term, do that. You can pull out that number to the front, as an overall constant, and just use the trial and error method from #1 to factor the remaining x^2 expression (if it can be factored). For example, for 2x^2 + 4x - 14, the leading coefficient 2 can be factored out from every term, so that it becomes 2 (x^2 + 2x - 7).

Say that you're asked to factor the expression 3x^2 + 4x - 16. Since the coefficient 3 can't be factored out from every term, we try to use the magic X method to factor. For the X box you draw on the side, the top number will be the product of the leading coefficient, the first number, times the constant at the end, negative 16. 3 times -16 is negative 48. The bottom number in your X is the second term’s coefficient, positive 4. Then at that point, look for two numbers that multiply to the top number, -48, and add to 4. List out the factors that multiply to -48 and check which ones add to positive 4. Since none of those add to positive 4, in this case the magic X did not help you factor. Why? Because the problem could not be factored.

For those of you who've learned about the discriminant, another way to tell whether a quadratic can be factored is to find the discriminant number, which is D = b^2 - 4ac, where a, b, and c are the coefficients and constant in your quadratic, ax^2 + bx + c. If the D value you calculate is either 0 or a positive perfect square number, then the quadratic expression can be factored.

Again, for factorable problems that CAN be worked out to completion, go to the intro factoring video mentioned above.

Editor: Miriam Nielsen of zentouro @zentouro

[daithi]

I hope we don't have to wait for another year to get another video.
Nancy is easily one of my favorite Math Youtubers, and over half a million people apparently agree.

[matildamoonga]

Omg Nancy! Welcome back 💕. You've been awfully missed.
Seriously hate math a little less thanks to your extremely helpful videos.

[jennifervercezes]

Nancy, idk if you may still come back to the channel, but I came to say:
Love your work here, as a physics major I'd like to see the continuation of calculus from you. ❤

[FMFvideos]

please come back! numbers doesn't make any sense without you

[nerdygiant]

This woman helped me get through college algebra years back. I didn't realized I hadn't subscribed until you popped up with this video. Nancy, please keep popping out more videos. I might not be taking the class anymore but I still enjoy the content.

[sonasunny]

You don't know how much you are helping us. I literally cleared my maths papers only because of you! You literally saved me in highschool and now in college. Thanks for everything.

[Mandark]

I've got a degree in mathematics already, but for some inexplicable reason I just can't resist the urge to watch this video on factoring quadratics.

[MrUtheChillWind]

Welcome back. Not a mathematician, but I love math and you give great quick explanations.

[tyblue]

Nanc, you make math understandable, which my professors fail at. I would LOVE to see you continue on with math videos (specifically calculus 1-3). I know it takes time and work to make these videos so I am prepared to buy you all the pasta, just please come back!

[yansantiagosiregar]

heyyy theree Nancy. I'm a student in Indonesia, and I'm facing AS level examination right now, and btw, I LOVE your videos💗💗💗, and it honestly helped me through my igcse times, and I'm so grateful for it. why haven't you made any videos lately? I'm really hoping to see more insightful videos especially for us students that is going through examination right now. THANK YOUUU SO MUCHH🙏🙏

[AmberWolf]

I don't even need to learn about factoring quadratics. I was just happy to see you posted a new video! You were a life saver during my college algebra classes. Thanks for all you do and welcome back : )

[CarlosMartinez-jovl]

Nancy’s return just made my day, thanks a lot for the content and we really hope you continue making these awesome videos

[Lynxxezz]

I really hope you come back. You just make learning math miraculous. You're really funny and lively. I wish you could do stuff like cubic functions and calculus. We hope you're doing well. We all miss you NancyPi 😢

[solvemathspace]

This class is a masterpiece! Your teaching style is so enthralling that it sparks curiosity and fuels a deep desire to learn more.

[tkcphoenixk]

My kids were just working on homework that had a quadratic that couldn’t be factored and we couldn’t figure it out… this video saved our sanity.

[CiedJacaba]

Two things I learned from this video:
1. some Quadratic Equations could be unfactorable
2. Nancy is human

[Lemuis]

The algorithm brought me here. Your math didactic, your marker wizardry, your soothing confident voice…I’m crushing hard. 🤩😍 Great channel!

[DRYusuftheGreat]

My teacher, I will be always grateful for you, you got me through so much in high school. from a 1st year student of medicine.

[vincentortega]

Welcome back Nancy, you have helped me so much with your awesome teaching. Glad you're back Nancy.

[kaibelzer]

i remember all of you’re videos when cramming for a algebra 2 placement test, glad you’re back