INSTRUCTORS Carleen Eaton Grant Fraser Eric Smith

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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?
5xy4 − 3x3y + 2xy
yes; trinomial
Is the following a polynomial? If so, is it a trinomial or binomial?
6x5y2 − 4x3y3
yes; binomial
Find the degree of
7x2y4 − 5rs5t + 4g4
degree = 5
Find the degree of
2a3b4c2 + 9g7h4 − 5g6
degree = 7
Find the degree of
3j4k2l6 + 4m5n − rs6t
degree = 6
Write in increasing powers of x:
7x5y4 − 4x3y5z + 12x8 − 9
− 4x3y5z + 7x5y4 + 12x8 − 9
Write in increasing powers of a:
2a4b5 − 3a5b2c4 − 5a2c6 + 9a − 12
9a − 5a2c6 + 2a4b5 − 3a5b2c4 − 12
Write in increasing powers of r:
5r4s6t3 + 6r7s2 − 4r3t3 − 8
− 4r3t3 + 5r4s6t3 + 6r7s2 − 8
Write in decreasing powers of d:
8d2e5f6 − 9d7e3 − 4d6f4g + 10
− 9d7e3 − 4d6f4g + 8d2e5f6 + 10
Write in decreasing powers of n:
7m2n3o − 13m4n5 − 6m5n2 + 11
− 13m4n5 + 7m2n3o − 6m5n2 + 11
Write in decreasing powers of m:
7m2n3o − 13m4n5 − 6m5n2 + 11
− 6m5n2 − 13m4n5 + 7m2n3o + 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.

### 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