Question about monomials (made so confused now)

onesun0000

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Dec 18, 2018
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I came across this question from my niece's homework and it made us puzzled.

"Is it possible for a 2nd-degree monomial to have 3 variables?"

Why puzzled? Well, at first it sounded so simple since I think monomials with 3 variables should be in 3rd-degree. and then I remembered this"6p^0qr". It almost destroyed my standpoint but thank goodness, I thought since p^0 is 1, it's still impossible to have 3 variables. Since I am still uncertain and want more answers, I posted this to a site and one of the users answered that it's possible if we consider the multinomial theorem.

What do you think?
 

pka

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Jan 29, 2005
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I came across this question from my niece's homework and it made us puzzled.
"Is it possible for a 2nd-degree monomial to have 3 variables?"
Why puzzled? Well, at first it sounded so simple since I think monomials with 3 variables should be in 3rd-degree. and then I remembered this"6p^0qr". It almost destroyed my standpoint but thank goodness, I thought since p^0 is 1, it's still impossible to have 3 variables. Since I am still uncertain and want more answers, I posted this to a site and one of the users answered that it's possible if we consider the multinomial theorem.
I think the answer depends upon the author of any particular textbook.
That said, have a look here.
 

Jomo

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Dec 30, 2014
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3,045
I came across this question from my niece's homework and it made us puzzled.

"Is it possible for a 2nd-degree monomial to have 3 variables?"

Why puzzled? Well, at first it sounded so simple since I think monomials with 3 variables should be in 3rd-degree. and then I remembered this"6p^0qr". It almost destroyed my standpoint but thank goodness, I thought since p^0 is 1, it's still impossible to have 3 variables. Since I am still uncertain and want more answers, I posted this to a site and one of the users answered that it's possible if we consider the multinomial theorem.

What do you think?
Well, at first it sounded so simple since I think monomials with 3 variables should be in 3rd-degree. I think that you meant to say at least three. After all, you could have -11p7q4r2 which is of degree 13.

Now onto your question. Yes, the degree of 6p^0qr is 3 and it does have 3 variables. However in the end I do agree with pka that it depends on how the author/teacher defined a monomial and its corresponding degree.
 

Jentis

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Feb 1, 2019
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Is there a usual way how to define a monomial and its corresponding degree in a case like this?
 
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