Help finding the degree of a polynomial?

Question

Given the expression –10p2q + 7p3q – 5q, do the following as instructed below:

Write the polynomial in descending order.
Classify the polynomial by the number of terms.
State the degree of the polynomial.

 

I already got that the descending order is 7p^3q - 10p^2q - 5q and that it's a trinomial but I can't figure out the degree of the polynomial.

Answer 1

We can factor out a q.

 

q(7p³ - 10p² - 5)

 

 

The larger polynomial has a degree of 3.  The smaller polynomial has a degree of 1.  Add these degrees together to a degree of 4.

 

 

Answer 2

The degree of the polynomial is the value of the largest exponent in it.

Since the largest exponent is 3, this is a third degree polynomial. We can also call it a cubic polynomial.