Finding the Zeros of a Polynomial

👉 Learn how to find all the zeros of a polynomial. 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.

To find the zeros of a polynomial, we first equate the polynomial to 0 and then use our knowledge of techniques of factoring polynomials to factor the polynomial. After we have factored the polynomial, we can then use the zero-product property to evaluate the factored polynomial and hence obtain the 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 term is equal to 0.

Timestamps:
0:00 Intro
2:52 Start of Problem

Corrections:
5:18 Forgot to substitute the x^2. There should have been 5 zeros for this polynomial: x= 0, \sqrt(2), -\sqrt(2), \sqrt(3)i, -\sqrt(3)i

Organized Videos:
✅Zeros of a Polynomial by Factoring
✅Zeros and Multiplicity of Polynomials | Learn About
✅How to Find all of the Zeros by Sum and Difference of Two Cubes
✅How to Find all of the Zeros by Grouping
✅How to Find all of the Zeros in Factored Form
✅How to Find all of the Zeros by Factoring 5th Degree
✅How to Find all of the Zeros by Difference of Two Squares
✅How to Find all of the Zeros by Factoring 4th Degree
✅How to Find all of the Zeros of a 3rd Degree Polynomial
✅How to Find all of the Zeros Without Factoring

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[cboisandlin]

Thank you random guy from 2012 for helping me with my math.

[knos]

The solutions you got in the end are the squares of the actual solutions, because earlier you substituted x^2 for x. The right answers therefore are the squareroots of 0, 2 and -3. So 0, sqrt(2), -sqrt(2) are correct for reals. Then there are two more imaginaries isqrt(-3) and -isqrt(-3). You should use a different letter than x for substitution to avoid this mistake

[UglyStru]

Uhm, why were you able to just straight up remove exponents to make it easier?

[flaps]

Let me guess... You are here because it's the night before a test and you procrastinated on studying? Yeah, me too

[sayunts]

Apply different letters for the substitution, such as x square equals t.

[vinceiii]

This made doing this so much easier thank you

[iamleaf]

this guys videos are so short yet teach so well so it helps me get through my stuff so much faster

[andrewm]

Sir, you forgot to finish your substitution! There are 5 solutions. But you only came up with 3.

[tasneemahmed]

when you take the original function and subtitue the zeros you got with x the 0 works out, but the -3 and 2 don't. Actually when I did this myself the zeros i got were 0, teh square root of 2 and the negative square root of 2. I don't get how on earth you got -3 and 2 from. Try them out, you'll get -252 and 28 which clearly are not zeros of that function.

[abdellaalou]

Sorry but it's wrong
Power 5 means 5 zeros
We get 3 reals and 2 Imaginary
Reals: -sqrt(2), 0 and sqrt(2)
Imaginary -isqrt(3) and +isqrt(3)

[azzar.]

I think this is wrong, u forgot to replace the substitutions with the actual values. When u set that equal to zero u get plus or minus root 2, also imaginary number. When u graph it the zeros are negative root 2, positive root 2, and zero

[dustinemagtibay]

I have a question
Is the answer supposed to be the equation to make the f o x/ domain / y intercept equal to zero like the first example to illustrate the principle but why it doesn't became zero when I substitute it to the equation or there are another things to consider checking in trinomial that I didn't
This is a question to make my mind clear
And thankyou for answering

[cloudian]

thank you so much, helped before my test!

[suryakamalnd]

Holy!! It's 11 years old! Guys watching this 1 day before exams
👇

[asiavf]

Hey happy new year. can you do these 8 math problems for me real quick? I already got the answers I just need you to work out how you got the zeros. Help me out I need to graduate this year

[gabrieldarlington]

thank you so much. YOu have made my life easier.

[JPEGMAFIA]

what are we gonna do if the coefficient cant be factored like 2x?

[AdamGeest]

X to the fourth equals the answer to mankind's deepest questions. I hereby decree this by mathematical fiat. hahah!

[stupidni-]

When and how the *fuck* is this gonna help me in life?!🗿

[its_jeonsa]

I have a teensy tiny doubt, so kudos to whichever random person helps me out later.


Soo, at 4:03 why’d he substitute x.4 to x.2 and x.2 to x? I mean, as far as I’ve learnt math (I’m a 12-year-old) anything can work as long as you don’t mess with the value. But here, the value has changed right? And he didn’t add it later on or something- can anyone pls make time to explain? - 😭✋