Given One Zero or Factor Find the Remaining Zeros

👉 Learn how to find all the zeros of a polynomial given one complex zero. A polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The zeros of a polynomial are the values of x for which the value of the polynomial is zero. Note that when a complex number is a factor of a polynomial, that the conjugate of the complex number is also a factor of the polynomial.

To find the zeros of a polynomial when one of the zeros is known, we use synthetic division to divide the polynomial with the given zero or we use long division to divide the polynomial with the given zero expressed in factor form. This gives the other factor of the polynomial, which can be further factored by dividing with the conjugate of the complex number and then further factored (if need be) using any of the techniques for factoring polynomials.

After we have factored the polynomial, we can then use the zero product property to evaluate the factored polynomial and hence obtain the remaining zeros of the polynomial. Recall that the zero-product property states that when the product of two or more terms is zero, then either of the terms is equal to 0.

Organized Videos:
✅Find all the Remaining Zeros Given a Factor or Zero
✅Find all the Remaining Zeros Given one irrational Zero
✅Find all the remaining zeros given one complex zero
✅Find all the remaining zeros given one rational zero

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#polynomials #brianmclogan

[MP-imun]

1 hour and 20 minutes of headache by my teacher vs 6 minutes of you going over a lesson ... seriously could be homeschooled for precalc by watching your vids

[raymondc]

Isn't it kinda funny how my textbook can't just explain this simply but Brian can?

[ivancristanchoplata]

Thank you Brian, i'm from Colombia and i couldn't find a video about this in my native language, but with you i could understand perfectly, a hug

[jeffreyjin]

a ad pop up and says does these videos from 2013 really helps? Me after watching this video is like, man it actually did and did very well.

[tylerc]

Thank you so much Brian! Your videos have been saving me from failing online school this year

[emmanuelsepulveda]

Thank you, thank you, thank you! I'm in college right now using a program called aleks and I was stuck with this kind of problem for an hour even with the explanation that they give (which evidently is not a good explanation) probably because they leave out certain steps or something but I come here and I fully understand the concept. Thank you so much!

[chelsea]

what does it mean if you have a remainder after doing long division? have i done something wrong?

[shaylaboben]

If i pass my test tommorow it will be because i learned from watching your videos. HUGE HELP

[lizbethmartinez]

Sir, you are going straight to heaven because you are a saint! thank you so much for these videos, I don't think anyone is truly bad at math, they just haven't had the right mentors

[laraozdogan]

thanks man, you explained this waaayyy better than my teacher😁

[Lex-jcdh]

what do you do if there is a remainder?

[TheInterestingInformer]

you are a real one, bro, thanks for this.

[javikia]

Awesome than Mr. McLogan goes back to his older videos and still leaves replies on the cooments

[julianas.]

Oh haha, this is the exact same problem I was working on.