How to Find Real Zeros of Any Polynomial Function

By finding the potential zeros and checking, we can find one of the real zeros. (If it exists) Depending on the degree of the function, we can use the same method to find the 2nd zero or factor the function to find the rest of the zeros.
The lesson also includes a quick lesson on using the synthetic division to check if a number is a zero of the function.

[@JadeLivao]

finding real zeros of a polynomial with synthetic division in a super approachable way. The step-by-step walkthrough makes the process clear and easy to follow, perfect for anyone tackling this topic!

[@Calculas4physics]

Make a series on calculs please sir

[@jacobbelury3417]

This was in algebra 2 for like 1 week barely a day lmao

[@yassertariqvideo]

Thank you the refresher. I am glad I started 2025 with your video, happy new year.

[@steveschmidt5156]

Outstanding. Thank you.

[@kenda-o3o]

I am an Arab student and I have benefited a lot

[@Unkown-Identity-h4u]

Thank you for this task.
If you reduced it to a quadratic funktion, the abc-formula is also an option.

[@kileyslife7541]

Thanks very much. I missed class so I was super confused on the hw

[@charlesrobinson3977]

You say this method works for "any polynomial function", but don't you mean "any polynomial function with integral coefficient"?

[@anestismoutafidis4575]

2•1^3 +11•1^2- 7•1 -6 =0
First zero-number=1
(2x-7/x)•(x^2+5,5x)+32,5 =>
(2x-7/x) 2•1,87 -7/1,87=3,74 -3,74=0
Second zero-number: 1,87
(x^2+5,5x) (-5,5)^2 +5,5 • (-5,5)=0
Third zero-number= -5,5
Zero numbers{ -5,5; 1; 1,87}ℝ

[@rokrok27]

This is rational root theorem , no ?

[@gregnixon1296]

My school system kicked the rational root theorem to the curb last year. Sad days.

[@davidnewell3232]

Mind your "p"s and "q"s.

[@NameFirst-jv9gj]

😂😂😂

[@josephshaff5194]

👍

[@geremymuccleswood307]

imagine p is 100 and q is 16…

[@carultch]

In that case, your candidates for roots would be:
1/16, 1/8, 1/4, 1/2,
5/16, 5/8, 5/4, 5/2,
1, 2, 4, 5, 10, 20, and 100
And the negatives of all of the above.
Usually, you try to use other clues as well, such as Descartes' rule of signs, and the sum and product of the roots, which can be directly determined from the b-term, the final constant term, the a-term, and whether the degree of the polynomial is odd or even. This allows you to narrow down your search for possible roots.
Polynomial roots in general, will add to -b/a, and will multiply to k/a for even-ordered polynomials, and multiply to -k/a for odd-ordered polynomials.

[@Mathgoddesssupports]

❓🙋‍♂️❓Why in the synthetic division do you multiply and then *add*? I see that it works but don’t understand why it does since division generally involves multiplying and then subtracting. TIA for anyone’s clarification.

[@carultch]

What synthetic division does, is replace operations such as subtracting a negative, with adding a positive. It recognizes the self-cancellation of the negative signs, and replaces it with the more intuitive operation of simple addition, and simple multiplication. It makes it so you don't need to guess terms, but sets them up in a more straight-forward method of calculating them