Factor Polynomial Given a Complex / Imaginary Root

[@MegaMark0000]

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[@RainbowArtzHD]

Whaaaa, is everyone getting the same ad over here

[@socaljusticewarrior558]

Underrated math channel. Left handed man is brilliant

[@youwhat.]

Much faster than what my teacher taught us. She wanted us to divide the whole polynomial by complex numbers twice.

[@mattemen36]

you forgot to write the the factors out completely at the end. You only wrote the zero's which is fine but you didn't write them in factored form. It should be (x - 4)(x + i)(x - i) in the end.

[@tajbibishamim8085]

Your g(x) is x-4 You got x^2+1 So just copy the p(x) Then leave one line and work the answer out like this x(x^2+1)-4(x^2+1) (x^2+1)(x-4)

[@thenozar7603]

You literally explained this so freaking well. Thank you soo much

[@aviarora2325]

hi

[@ciaragibson1371]

How could you do something like this if you are not given all the coefficients of the polynomial, for example there is an unknown “p” in front of the x^2 and you are only given the complex roots?

[@muadiib7562]

So I have an issue where I'm trying to factor a polynomial, f(x)=8x^4 - 100x^3 + 535^2 - 232x-61 where the root is 6-5i... literally nobody seems to be able to help me and I'm freaking desperate.

[@isaiahsolis8456]

Lmao a whole year and know help

[@socaljusticewarrior558]

Well, let's try to help him even though it is much too late. It is still the right thing to do.

[@Anaheim2011]

Thank you omg I needed this (:

[@crunchypopkorn]

Well I kinda dont get the part - given 'i' is zero then x+i and x-1 factor ?

[@on1zukas3ns31]

Thank god for this video.. you sir just secured 10 points on my grade!

[@adejareojo]

there are some cases when you conjugate the numerator instead of the denominator if the top has a radical in it.

[@adrianavelasco8501]

why can't you use synthetic division?

[@UnequalJumper]

You Sir, Thank you so much. A better teacher than mine own.

[@socaljusticewarrior558]

Is this above algebra two? What the heck? My book is only asking me to name the conjugates of the given roots. I want to factor a polynomial like Patrick did.

[@ryanhutzel7897]

im given 4 +8i how do i do that thers no x

[@deepanshugoyal8286]

so lengthy solution..just write sum of roots =4=i+(-i)+ a , hence a=4

[@vikramkarmarkar1617]

what would you do if you were given a factor or (-2-root2)

[@incodewetrust8862]

why you write x0+1 i don't get it because if i dont write normal x^2+1 my R=-2x

[@brainlover7764]

Thanks!...I found it easier to use synthetic division though,also got x-4

[@muntoo1]

Hi - good video but can you help me with this:2-i is a root of 2x^4-23x^2+44x-5; find other 3 roots

[@high5en]

My brain just exploded...and I'm about to fail a test tomorrow morning.

[@metaman8662]

I'm completely lost :(

[@deliabrown3509]

What if you have a root like (x-1+2i) and (x-1+2i)? When you multiply them together it doesn’t work out cleanly. You get ix

[@patrickjmt]

imaginary roots always occur in conjugate pairs

[@TheMNHShow]

Good tut, but I have one big problem: what if I'm not given any roots?

[@RevoltBlackOps]

Then "guess" a root, try with the simple ones, i, -i, 2i, -2i.

[@RevoltBlackOps]

Of course, it is enough that you guess only positive or only negative purely imaginary roots.

[@ManishSuryapalamSTEM]

Why is x+i a factor as well?

[@cadenlin1643]

Conjugate pair theorem states that if a+bi is a root, a-bi must also be a root(and vice versa). So if 0+1i is a root in this case, 0-1i must also be a zero.

[@quangngo4575]

Love you patrick

[@barbegazi3635]

This was so helpful, thank you!!

[@Hellii0]

this is gonna save me on my big exam tomorrow because our book is just crap.

[@leah7158]

Trying to find a frame where his hand doesnt cover 75% of the actual problem

[@patrickjmt]

good luck with that

[@Wolfpup098]

Thank you!

[@COURTANAYsayshey]

you save lives

[@meowymeow950]

Thanks a lot sir 😄

[@Shuey272]

need more pixels... (a few moments later) *phew*

[@morgengabe1]

Leave zero's eyes alone!

[@PhanteusZ]

THAAANK yOOOOOOOOOOOOOOu

[@YouToBeVP]

nice man thnx

[@azizizizi1404]

A "zero" really confused me alot

[@Prodigyfer]

thanks man :)

[@HarrisonInman]

good video

[@danis.5922]

I am very much confused 😺

[@TGPadm]

awsome

[@Shineinpoverty]

like like like like like (dont like math though)