Question

Write down the degree of each of the following polynomials:
$7x^3-5x^3{y}^2+4y^3-9$

Answer 1

We know that the degree of each term in a polynomial in two variables is the sum of the exponents in each term and the degree of the polynomial is the largest such sum.

Let us first find the degree of each term of the given polynomial $7x^3-5x^3{y}^2+4y^3-9$ as follows:

$7x^3$ has a degree of $3$ ($x$ has an exponent of $3$)

$5x^3{y}^2$ has a degree of $5$ ($x$ has an exponent of $3$, $y$ has $2$, and $3+2=5$)

$4y^3$ has a degree of $3$ ($y$ has an exponent of $3$)

$9$ has a degree of $0$ (no variable)

The largest degree in the above terms is $5$.

Hence, $5$ is the degree of the polynomial $7x^3-5x^3{y}^2+4y^3-9$.