What is the degree of this monomial 17x^5y^2
2 answers:
The degree of this monomial, which is a form of a polynomial, has a degree of 7.
Explanation: For two variables, we take the sum of the powers and this becomes the highest power of our polynomial, which is defined as the degree of a polynomial.
Now, it's relatively easy for polynomials where we are taking one variable, but two variables is a little bit harder.
Notice how any variable to the power of 0 will give us 1, and anything multiplied by 0 will give us 0.
We can rewrite this in many different ways:
![17x^{5}y^{2} = 17x^{5}y^{2} + 0x^{6}y^{4} + 0x^{4}y^{6} + [...]](https://tex.z-dn.net/?f=17x%5E%7B5%7Dy%5E%7B2%7D%20%3D%2017x%5E%7B5%7Dy%5E%7B2%7D%20%2B%200x%5E%7B6%7Dy%5E%7B4%7D%20%2B%200x%5E%7B4%7Dy%5E%7B6%7D%20%2B%20%5B...%5D)
Since every other factor cancels out to be 0, then we say that they are non-existent, because even, if in hindsight they do exist, they don't affect our final polynomial.
So, we can say that the degree of this polynomial, highest power, is 7.
Explanation: For two variables, we take the sum of the powers and this becomes the highest power of our polynomial, which is defined as the degree of a polynomial.
Now, it's relatively easy for polynomials where we are taking one variable, but two variables is a little bit harder.
Notice how any variable to the power of 0 will give us 1, and anything multiplied by 0 will give us 0.
We can rewrite this in many different ways:
Since every other factor cancels out to be 0, then we say that they are non-existent, because even, if in hindsight they do exist, they don't affect our final polynomial.
So, we can say that the degree of this polynomial, highest power, is 7.
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