Question

What is the degree of this monomial 17x^5y^2

Answer 1

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) + [...]`

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.

Answer 2

Sorry i misread the degree is 7 add the exponents to get the degree of a monomial my bad sorry...