Don't Set Up Systems of Equations - There's a Better Method

It might be tempting to write a system of four equations from the quartic polynomial, but there is a method to greatly simplify calculations and arrive at our answer faster!
For anyone studying polynomials, this is a great problem to help exercise their problem solving skills, as well as for those preparing for math competitions. Getting better at math is not just about knowing more, but mostly how we can apply what we know to learn more.
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[@CompassMathematics]

I'm aware that we can just plug in x=1,2,3,4 and obtain a system of four equations with four variables, but this method proves to be quicker with its simplicity. For instance, if I gave similar information with a degree 10 polynomial, I don't think we'd be setting up systems of equations :)

[@samagraarohan2513]

This is clever!

[@dan-florinchereches4892]

That was a nice manipulation. Pretty handy if to find some formulas you do not remember. I was thinking about sum i=1 to n of i^0 = n Sum i=1 to n of i^1 = n(n-1)/2 Conjecture sum of i^k is going to be a polynomial of degree k+1 and find coefficients then do mathematical induction. This makes finding coefficients much quicker

[@CompassMathematics]

great idea!

[@Teraverse420]

Pretty Underrated Channel!

[@ShanBojack]

True just found about this channel

[@tulipawrongzhao6142]

Awesome video, really enjoyed it. +1 sub, will be watching others Hope you keep going💪

[@ShanBojack]

Gained a subscriber ❤

[@youssefmaged8368]

Great channel and great video. Subscribed

[@maryoomOubah]

oh