Find All the Zeros using P Over Q Rational Zero Test

👉 Learn how to find all the zeros of a polynomial that cannot be easily factored. 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 that cannot be easily factored, we first equate the polynomial to 0. Next, we 'guess' one of the factors of the polynomial and then use synthetic division or long division to find other factor(s) the polynomial. After we have obtained the factors and have factored the polynomials, we can then use the zero-product property, quadratic formula or any other applicable property or formula to evaluate the factored polynomial and hence obtain the zeros of the polynomial.

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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[brianmclogan]

hey I am just happy I can serve students like you looking for how to solve a problem and not have to listen to an hour lecture or 10min youtube video. I have now organized all of my videos on my website for easy finding the right video as I have so many it's hard to find exactly what you want sometimes. Thanks for watching. I appreciate your comment

[Ardimento]

Ya know, you don't get many views on these videos... but as a student who needed help with this.... regardless of the number of views or likes-- its appreciated and I'm sure I'm speaking for many others when I say.

[jacksonh]

I could smell that sharpie thru the screen

[darkstride_underscott]

I uh. Don’t know what was going on at the beginning. I’m lost. Was there a video leading up to this? 😓

[amarabland-haynes]

I think that you forgot to include the -12x^2 when you were determining the number of negative zeros. You only forgot to include the exponent for the -12

[tumak]

Descartes would say that there could be 2 or 0 + real roots...you get 2 and then decrease by 2 to continue. This question would definitely keep you out of trouble if you check the fractions first.
Cheers

[EmmanuelBello]

how did you get the 1 negative that you used to divide them?

[BillyMinnow]

How do we find a zero without graphing?

[septube]

How is -5 and a -3 giving you -16? -5x-3=15 but how can those two numbers equal -16?

[Cassierox]

How do you list the factors of your leading coefficient if the problem is like:
 f(x)=x^3+6x^2+5x-3-12 ????  there is no leading coefficient?