Question

Given the expression 5a2b – 13ab + 7a3 – 4b, do the following as instructed below:

1. Write the polynomial in descending order.
2. Classify the polynomial by the number of terms.
3. State the degree of the polynomial.
Thank you !!

Answer 1

Ok, here is the answer:

A. The descending order of this expression is 7a^3+5a^2b-13ab-4b.

B. This is a polynomial.

C. This is a 3rd degree polynomial.

Answer 2

ANSWER TO QUESTION 1

The given expression is


`5 {a}^(2) b - 13ab + 7 {a}^(3) - 4b`

To write the polynomial in descending order means we should write in decreasing powers of

`a`


So in descending order we have,



`7 {a}^(3) + 5 {a}^(2)b - 13ab - 4b`


ANSWER TO QUESTION 2

When a polynomial is in simplified form and it has one term, we call it a monomial.



If a simplified polynomial has two terms,it is called a binomial.




If a simplified polynomial has three terms, it is called a trinomial.



If a simplified polynomial gas four or more terms, we just call it a polynomial.



The given polynomial


`5 {a}^(2) b - 13ab + 7 {a}^(3) - 4b`

has four terms and it us in simplified form, so it is classified as polynomial.



ANSWER TO QUESTION 3.

The degree of the polynomial is the highest degree the polynomial has.


We calculate the degree by adding the exponents of the two variables of each term.


For instance the first term is

`7 {a}^(3) = 7 {a}^(3) {b}^(0)`

`degree = 3 + 0 = 3`


Since the highest degree is 3, we say the degree of the polynomial 3.