Determine the degree of each polynomial. − 3 x 2 − 5 x 2 y 2 + y 3 -3x^2-5x^2y^2+y^3

So, many times in your expressions, you're going to run across terms that have multiple variables like x's and y's, just like our practice problem over here. We've got negative three x squared minus five x squared y squared plus y cubed and our task is the same we're going to determine the degree of this polynomial. So, remember that is the highest degree that we see of all the terms in this polynomial, so we're just going to go through one by one and identify the degree of each of the terms and then just pick the highest one. Starting with negative three x squared, now this is a term that only has a single variable, just x, so we can just go ahead and look through the exponents, and the exponent is two, therefore the degree of this term is just two. Alright, now let's take a look at the second term. Here, we've got negative five x squared y squared. We've got multiple variables x and y, so you have to sum all of the exponents and all the variables to get the degree. The degree of this polynomial is, or this term, is not two, it's four because we have two, sort of squares, for x and y in this term. Now, finally, we have gotten y cubed. This is only a single variable, just y. So, we look at the exponent and it's a three. So, this is a degree of three. So, now what we do is to find the degree of the polynomial. Just take a look at the highest degree out of all the terms. We can clearly see that it's to the fourth power. Again, this is a common misconception or common mistake that I see a lot of students making. They'll look through their polynomial and they'll just look through the highest exponent they can possibly find inside of all the terms, and they'll think that is the degree of the polynomial. So, many students would mistakenly think that this degree is three here, but because this two, this term has two variables, you have to add the exponents together, therefore making this a degree of four. Alright? So, that's the degree of this polynomial. Let me know if you have any questions. Great job if you got the answer right. I'll see you in the next one.

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Determine the degree of each polynomial.
$- 3 x^{2} - 5 x^{2} y^{2} + y^{3}$

$5$

$3$

$4$

$9$

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검증된 단계별 안내

Identify each term in the polynomial: $-3x^{2}$, $-5x^{2}y^{2}$, and $y^{3}$.

For each term, find the degree by adding the exponents of all variables in that term. For example, in $-3x^{2}$, the degree is $2$ because the exponent of $x$ is $2$.

Calculate the degree of the second term $-5x^{2}y^{2}$ by adding the exponents: $2$ (from $x^{2}$) plus $2$ (from $y^{2}$), which gives a total degree of $4$.

Calculate the degree of the third term $y^{3}$, which is simply $3$ since the exponent of $y$ is $3$.

Determine the degree of the entire polynomial by selecting the highest degree found among all terms, which is the maximum of $2$, $4$, and $3$.