1. Polynomials
Chapter 8.4

2. Polynomials
Lesson Objective: NCSCOS 1.01 – Write the equivalent forms of algebraic expressions to solve problems
Students will know the terms for polynomials.
Students will know how to arrange polynomials in ascending and descending order.

3. Polynomials
Monomial – a number, a variable or a number and variable multiplied together. Ex: 3, x2, or 5x
Polynomial – a monomial or sum of monomials. Ex: 2, x, 3x2 + 2x
Binomial – the sum or difference of two monomials. Ex: 3x2 + 2x
Trinomial – The sum or difference of three monomials. Ex: 3x2 + 2x – 7
*Numbers that are being divided are not monomials or any of these types of problems. Ex: 2/x is not a monomial, polynomial, binomial, or trinomial!

4. Polynomials
Ascending order – increasing from the smallest to the largest. Ex: 1, 3, 4, 6, 7
Descending order – Decreasing from the largest to the smallest. Ex: 8, 5, 4, 2, 1
*When re-ordering a problem into ascending or descending order use the exponents (powers) of the variable to determine which goes first.

5. Polynomials
Example 1:
Arrange the terms or each polynomial so that the powers of x are in ascending order: x4 – x2 + 5x3
Answer: – x2 + 5x3 + x4

6. Your Turn! Polynomials Write in ascending order: 8, 16, 2, 6, 21, 0
2x3 + 3x5 + 4x
5x2 – 6x4 + 2x3
23x8 + 14x5 – 34x2
Your Turn!

7. Polynomials
Example 2:
Arrange the terms or each polynomial so that the powers of x are in ascending order:
8x3y – y2 + 6x2y + xy2
Answer: – y2 + xy2 + 6x2y + 8x3y

8. More Problems Polynomials 2x2y3 + 3x3y6 + 4xy 5x7y5 – 2x2y4 + 7x4y2
Put the following in ascending order according to the x value.
2x2y3 + 3x3y6 + 4xy
5x7y5 – 2x2y4 + 7x4y2
12x4y2 – y5 + 3x + 8x6y3
More Problems

9. Polynomials
Example 3:
Arrange the terms or each polynomial so that the powers of x are in descending order: x4 – x2 + 5x3
Answer: x4 + 5x3 – x2

10. Try Again! Polynomials Write in descending order: 8, 16, 2, 6, 21, 0
2x3 + 3x5 + 4x
5x2 – 6x4 + 2x3
23x8 + 14x5 – 34x2
Try Again!

11. Polynomials
Example 4:
Arrange the terms or each polynomial so that the powers of x are in ascending order:
8x3y – y2 + 6x2y + xy2
Answer: 8x3y + 6x2y + xy2 – y2

12. Last Try Polynomials 2x2y3 + 3x3y6 + 4xy 5x7y5 – 2x2y4 + 7x4y2
Put these in descending order according to the X value
2x2y3 + 3x3y6 + 4xy
5x7y5 – 2x2y4 + 7x4y2
12x4y2 – y5 + 3x + 8x6y3
Last Try

13. Quiz 8.4 Polynomials True or False: 3x2 is a monomial.
T or F: 5x – 2 is a trinomial.
Arrange in ascending order: 3x – 7 + 5x2
Arrange in descending order by the powers of x:
2x + 3x2 – 7
7xy2 – 5x3y + 2y4