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### Polynomials

- A
*polynomial*is a sum of one or more monomials. A*binomial*has 2 terms, and a*trinomial*has 3 terms. - The
*degree of a monomial*is the sum of the exponents in all its variables. - The
*degree of a polynomial*is largest degree of any term in the polynomial. - A polynomial is written is
*descending order*if the powers of one variable are in descending order. - Usually, polynomials are written in descending order.

### Polynomials

Is the following a polynomial? If so, is it a trinomial or binomial?

5xy

5xy

^{4}− 3x^{3}y + 2xyyes; trinomial

Is the following a polynomial? If so, is it a trinomial or binomial?

6x

6x

^{5}y^{2}− 4x^{3}y^{3}yes; binomial

Find the degree of

7x

7x

^{2}y^{4}− 5rs^{5}t + 4g^{4}degree = 5

Find the degree of

2a

2a

^{3}b^{4}c^{2}+ 9g^{7}h^{4}− 5g^{6}degree = 7

Find the degree of

3j

3j

^{4}k^{2}l^{6}+ 4m^{5}n − rs^{6}tdegree = 6

Write in increasing powers of x:

7x

7x

^{5}y^{4}− 4x^{3}y^{5}z + 12x^{8}− 9 − 4x

^{3}y^{5}z + 7x^{5}y^{4}+ 12x^{8}− 9Write in increasing powers of a:

2a

2a

^{4}b^{5}− 3a^{5}b^{2}c^{4}− 5a^{2}c^{6}+ 9a − 129a − 5a

^{2}c^{6}+ 2a^{4}b^{5}− 3a^{5}b^{2}c^{4}− 12Write in increasing powers of r:

5r

5r

^{4}s^{6}t^{3}+ 6r^{7}s^{2}− 4r^{3}t^{3}− 8 − 4r

^{3}t^{3}+ 5r^{4}s^{6}t^{3}+ 6r^{7}s^{2}− 8Write in decreasing powers of d:

8d

8d

^{2}e^{5}f^{6}− 9d^{7}e^{3}− 4d^{6}f^{4}g + 10 − 9d

^{7}e^{3}− 4d^{6}f^{4}g + 8d^{2}e^{5}f^{6}+ 10Write in decreasing powers of n:

7m

7m

^{2}n^{3}o − 13m^{4}n^{5}− 6m^{5}n^{2}+ 11 − 13m

^{4}n^{5}+ 7m^{2}n^{3}o − 6m^{5}n^{2}+ 11Write in decreasing powers of m:

7m

7m

^{2}n^{3}o − 13m^{4}n^{5}− 6m^{5}n^{2}+ 11 − 6m

^{5}n^{2}− 13m^{4}n^{5}+ 7m^{2}n^{3}o + 11*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

### Polynomials

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro 0:00
- What is a Polynomial 0:07
- Monomial
- Binomial
- Trinomial
- Degree of a Polynomial 1:56
- Example: Degree of Monomial
- Example: Degree of Polynomial
- Ordering Polynomials 3:32
- Example
- Example 1: Trinomial or Binomial 4:44
- Example 2: Find the Degree 5:27
- Example 3: Increasing Powers 6:11
- Example 4: Decreasing Powers 7:27

1 answer

Last reply by: Dr Carleen Eaton

Wed Jul 12, 2017 11:09 PM

Post by Ling Huang on June 6 at 02:50:12 PM

For example 3 in Ordering Polynomials, shouldn't 15 be first since it's 15x^0?

1 answer

Last reply by: Dr Carleen Eaton

Mon Nov 9, 2015 10:41 PM

Post by Manuel Ramirez on November 9, 2015

I need help with fraction 2 / 2x+1 + 6/12x+3 the 2 goes underneath 2x+1 and 6 underneath 12x+3 and you add

1 answer

Last reply by: Dr Carleen Eaton

Fri Aug 2, 2013 6:51 PM

Post by Yolanda Britt on August 1, 2013

how many numbers or variables does a polynomial have to have?

1 answer

Last reply by: Dr Carleen Eaton

Fri Jun 21, 2013 11:07 PM

Post by Taylor Wright on June 21, 2013

In example 3:

Isn't 15 the same as 15(x^0) ?

1 answer

Last reply by: Dr Carleen Eaton

Fri Jun 21, 2013 11:04 PM

Post by Taylor Wright on June 21, 2013

In ordering polynomials, why wouldn't it be written with the 2 in front, since 2 is also 2(x^0)