Could someone please explain this video in an easier-to-understand way? I've watched it several times, and still don't get how to find the rational roots of a polynomial =(
Thank you so much for your help!
Unfortunately you can not post a link here.
Oh, I didn't know that, I'm really sorry! The video is called "rational zeros test" and the youtube channel is "lfhsmah"
I could not find the one you said but this one seems pretty well explained:
https://www.youtube.com/watch?reload=9&v=Xsth3AEF7gk
Of course! I'm here to help you understand how to find the rational roots of a polynomial in an easier way.
To find the rational roots of a polynomial, we use a method called the Rational Root Theorem. Here's how you can apply this theorem step by step:
Step 1: Write down the polynomial in its standard form. For example, let's say we have the polynomial: P(x) = 2x^3 - 5x^2 + 3x - 1.
Step 2: Identify the coefficients of your polynomial. In our example, the coefficients are 2, -5, 3, and -1.
Step 3: List all the possible rational roots. A rational root always takes the form of p/q, where p is a factor of the constant term (in our case, -1), and q is a factor of the leading coefficient (in our case, 2). So, the possible rational roots for our polynomial are the combinations of the factors of -1 and 2.
For our example, the factors of -1 are: +1, -1
The factors of 2 are: +1, -1, +2, -2
So, the possible rational roots are: ±1/1, ±1/2
Step 4: Use synthetic division or long division to test each possible root. Start with the first possible root and divide the polynomial by it. If the remainder is zero, then that means this possible root is a rational root.
For example, let's test the possible root +1/1:
Perform the division:
2 | 2 -5 3 -1
| - - - - - - -
| 2 -3 0 3
The remainder is 3, which is not zero.
Now, move on to the next possible root.
Let's test the possible root -1/1:
Perform the division:
-1 | 2 -5 3 -1
| - - - - - - -
| -2 7 -10 11
The remainder is 11, which is not zero.
Continue this process for each possible root until you find one or more roots where the remainder is zero. Those are your rational roots.
Step 5: If you find a rational root, you can use polynomial long division or synthetic division again to further simplify the polynomial. This will help you find any remaining rational or irrational roots.
I hope this explanation makes it easier for you to understand how to find the rational roots of a polynomial!