Factoring 5-term polynomials by grouping

Learn how to factor 5-term polynomials by grouping.

Factor x^4-4x^3+2x^2-11x+12

[alexandermotley]

Thank you! The only video that really showed how to do this without an obvious GCF!

[renewd]

For anybody looking for a great book on factoring, I recommend Schaum's College Algebra outline. It doesn't give problems exactly like this, but it gives you a thorough education in fairly advanced factoring methods.
For the 2nd problem, I broke the 2x down to x + x, then I used factoring by grouping to get x^3(x + 1) + x(x + 1) + 1(x + 1), factoring out (x + 1), and my answer was (x + 1)(x^3 + x + 1). HIs method is probably a little more straightforward, but it's getting late and I somehow missed x^2 + 2x + 1, even though it was in the first problem.

[treeheet]

>Asian
>Holds and Uses 2 markers in one hand
>Wears supreme
>and oh, Good at math


is this God?

[spencel]

are we just going to ignore that this guy is wearing supreme

[parthasarathibehera]

We can use regrouping method for factoring this polynomial: x^4 + x^3 + x^2 + 2x + 1
Let's factor it.
(x^4 + x^3) + (x^2 + 2x + 1)
= x^3(x+1) + ((x)^2 + 2(x)(1) + (1)^2)
= x^3(x+1) + (x+1)^2
= x^3(x+1) + (x+1)(x+1)
= (x+1)(x^3 + x + 1)
Thank you so much.
Jai Shree Rāma.

[ChaseL]

A SUPREME quarter zip?? Teach me more master

[chrisg]

Cant focus, instructor has too much sauce.

Serious question: How do you go about factoring (x^3+x^2+1) if you need to find all the x intercepts (both real and imaginary)?

[ProteinFromTheSea]

A haiku
Great math tutor
it will get straight to the point
you have earned a sub

[ajeethbt]

I did it in a bit different way and came to the same answer
x^4 + 2x^3 + x^2 + x + 1
= x^4 + x^3 + x^3 + x^2 + (x + 1)
= x^3(x+1) + x^2(x+1) + (x+1)
=(x^3+x^2 )(x+1) + (x+1)
= (x+1)(x^3+x^2+1)

It looks big as I have written almost every step.

[matthewzuelke]

Step 1: plug into graphing calculator
Step 2: solve for x values

[pratyushsingh]

Man i was struggling for so long and found this vid
Keep going ahead.. Tysm

[MotivationCentral]

I see, as a fellow asian, that you are a man of culture as well.

[sadhnaupadhyay]

thanks very much I was really confused

[renujadecosta]

excellent... this video helped me a lot to solve a hard problem in V-T graphs.Although this factorization isn't i couldn't think of this at that moment until I saw your video.. thank you very much for this video.

[emmitcannady]

Thanks for actually teaching me my teacher doesn’t seem to be very good at that

[krishaarya]

Factorise – 6x^4 –25x^3 +12x^2 + 25x +6

[jonm]

This was so helpful in my differential equations homework.

[tropicocean]

5:14 And look at thiis!!!😂😂
Great Video

[TitanUnleashed]

what math do u learn this in. Im guessing thsi way isnt what im learnin yet in precal. I have to use potential rational roots way with synthetic division.

[mallowthefinal]

I ended up forgetting the question I was here for ‼️😂