Given One Complex Zero Find the Remaining Zeros of a Polynomial

👉 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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[betterexcel]

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[dookietooth]

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[imaginealot]

Oh my gosh, thank you SO much!! You have no idea how helpful this is, my math teacher does not know how to explain things in a way anybody would understand.

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Once again, your the only reason I’m passing pre cal.

[RaulRodriguez-tvsj]

I've had the hardest time getting this concept in class, thanks for posting!

[marymccory]

This video was a life saver, how can I find you doing other pre-calculus topics?

[sheeptaro]

I was lost in class, this helped me a lot. It was well explained. Thank you!

[lgm_nyk]

Another way you can do this problem is by FOILing (x-5i)(x+5i) to get x^2+25. You can then put that through long division, and still get 2x+3. I have always found this way easier because you deal with i less. But whatever works for you!

[rennywilder]

This is the same example that was on my homework. I promise I did it beforehand while watching another of your videos, but I was glad to know I did it right

[brianmclogan]

very common reaction. Happy to help you

[Marcoavargas]

Finals are next week. I have a lot of refreshing to do. Thanks!

[JBMotivation]

Great videos, they help a lot!! BUT how do you do this without synthetic division? My teacher doesn't let us use synthetic division. Do you have any videos showing without synthetic division? I can't find any.

[lams]

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[brianmclogan]

yes multiply the two complex factors by each other and then use long division.

[stevefarrell]

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[yesseniamartinez]

thank you so much! this made my math homework so much easier:)

[tpage]

Thank you so much for posting this video, I have learned more from you on here then I have from my actual teacher this year haha. Thank you for posting videos, you are a lifesaver!!!