Rational Roots Test / Theorem

Rational Roots Test - In this video I talk about how you can find all of the possible rational roots of a polynomial.
Note that to find the rational roots of a polynomial we simply look at all possible combinations of factors of the constant divided by factors of the leading coefficient.
Note that if there is not a constant, all terms involve some power of x. In this case FIRST factor out the smallest power of x and then use the rational roots test on the remaining factored polynomial.
Once you have all of the possible rational roots it is just a matter of substituting each candidate into the original polynomial to see if any of these values give zero after simplifying.

#maths #patrickjmt #rationalroots #factorial #polynomials #zeroes #zeroesofpolynomial

[arav]

I was three year olds when this video was made. Now this same video is helping me 11 years later

[pizzafreak]

I swear! This man saved me from going insane and failing my Algebra 2 class during the summer! The teacher was so awful. Thank you!

[patrickjmt]

Hi all! Please post comments, questions and anything else on your mind in the comment section! Also, don’t forget to LIKE, THUMBS UP, and SUBSCRIBE! I’d appreciate it greatly :)

[aryashivakumar]

at 4:12 you said "you get negative five" but the numbers are 2 and -3, so 2-3-11+6=-6, still not zero, but just clarifying in case anyone else caught that

[jvaniee]

Use the rational roots test and then plug the possible roots back in the polynomial to see if they = 0. Or, like what your professor did use the possible roots and the polynomial in synthetic division. If the remainder is 0 then it's a root. Both ways work but it'll probably be faster to do synthetic division.

[stormzsamurai]

This video is helpin saving my grade in alg 2 rn. Thank you so damn much man. I have no idea when this came out but im so happy this is here!!

[nespecialistin]

Man, you explain math better than all of the math teachers that I used here in Bulgaria. Thanks bro!

[sirruffalot]

Patrick...I love you.. I've been watching your videos for quite some time now, you helped me through algebra, stats, precalc, calc etc..

[patrickjmt]

if you are using real numbers, one can not just look at the degree and conclude the polynomial has that many roots.
consider f(x) = x^2 + 4

this has no roots (again, using real numbers).
the degree is the maximum possible number of real roots.
euler (i think) proved that there will be n solutions (some repeated) to a n degree polynomial if we use complex numbers - it was his phd thesis!

[thelasagneman]

goes through 12 years of math, never hears of this, hears it, is ever so grateful, you sir are a legend!

[tanggapandaniela]

Correct me if Im wrong, isn't it 2-3-11+6=-6?? Not 10? From the first equation u gave.

[aadidesai]

5:31
54-27=-27
-27-33=-6
-6+6=0
Nice for you to help us, but please recheck work. + for the effort

[andreadelossantos]

I think it's not -27-33+6 it should be 27-33+6. Just get rid of the negative sign in 27 .

[NeatherBen]

This guy saved me from failing my Algebra 2 class during this year! The way the Connexus program is so sketchy! Thank you so much!!!

[patrickjmt]

yes, first factor out the x.

then you can use rational roots thm on the polynomial of degree 6

[chloecox]

Your videos are a blessing for me during this covid 19 crisis. THANK YOU!!!

[Mahmzo]

It seriously annoys me how I learn concepts in under 3 mins on this channel 😂😂

[vetacoth]

You are the best math teacher on YouTube. Without you, I would have failed so many classes but I have to ask, when will this ever be applied to life?

[miker]

Studying day before major assessment. This is the best vid I found after an hour of looking. Thanks man

[ShrimpWizard]

You saved my Math grade, Sir!! Thank you so much for such an awesome video!!