ʕ•ᴥ•ʔ What is a Polynomial Explained Properly.. Finally!

There are criteria for expressions to be called polynomials. A polynomial needs to have at last 3 algebraic terms. For instance, an expression with negative exponents is not a polynomial. In this lesson, we will also learn how to classify polynomials base on their number of terms.

Hi, welcome to this question here. So we're trying to determine which is the polynomial, right. So the key idea is this; all you have to do is focus on the variable like x, y, z, a or b's; and exponent of that variable must be a whole number, okay. So, if it's known, for example it's a negative, it's like a fraction then it's not considered as a polynomial, okay. So let's take a look at the first one, 6. Is 6 a polynomial? It actually is because what happened is, if you just pretend there's a X power zero; and zero is a whole number, okay. So, that's equivalent as 6 x 1 because anything to the power zero is a 1, so it is still 6. So any constant number is considered as a polynomial, okay. So, it will check mark right there. The second one, don't worry about the root 3 just worry about the variable X and that is just a 1 on the top, so, check mine for that. This one over here is X to power 1/3. A-ha! It's not a polynomial because we cannot have a fraction, okay. So because of that this is not a polynomial. Aah, there's "b" b to power 3, there's a "b" to power 1; they're all whole numbers so that's a check mark right there. This one over here, that one is okay. This one here it's not okay because the Z over here, technically, it's a Z to the power one half, okay, because it's a square root; we can change it into exponential forms. So it's just a fraction, so again this, you cannot have a fraction so this is not a polynomial, okay. We'll cross right there. That one is kinda obvious, it's a power of -4 and it's not a polynomial, so this will cross right there. The last one is a bit tricky because you do see that's X to the power 1, right. But because it's actually at the denominator. So if you rewrite this, this X can be put to the top, that's the X to the power of -1 and we know that in order to be a polynomial, you cannot have exponent as a negative for the variables. So in this case, this guy right here is not a polynomial, okay. Hopefully it helps you and thanks for watching.

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[ramyresdavid]

I am intrigued on how he writes. I mean look the way he writes.

[irisbantillo]

When im a year away from college but still got to learn this...

[supersql]

Just learn or remind myself I should say what a polynomial is from another Youtuber, but this video shared the secret sauce with the power of the exponent and what it means to be truly a polynomial! Thank you!

[ainyqureshi]

O wow😍 sir u make this so simple to understand👌 thnx alot

[thayasukinavasothy]

where do u get negative 1 exponent in the last question.That is the part of the question that I really confused about it sir.

[bannana]

If the 2nd one is a polynomial why is 4 not?

[mohammadzahid]

Finally found something really helpful....tnx sir.

[noonmichaud]

Getting caught up on homework. Really helped! Thanks!

[eduardvaldez]

wait the last one was still a fraction right

[manojkumarmishra]

Explained nice it helps me too much. Thanks

[Alfred-wghg]

I remembered that a constant is a Maybe the video teaches the opposite?