Chapter 8.4
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.
POLYNOMIALS
 Monomial – a number, a variable or a number and variable


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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!
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.
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
POLYNOMIALS
1. Write in ascending order: 8, 16, 2, 6, 21, 0
2. Write in ascending order:
1. 2x3 + 3x5 + 4x
2. 5x2 – 6x4 + 2x3
3. 23x8 + 14x5 – 34x2
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
POLYNOMIALS
 Put the following in ascending order according to the x
value.
1. 2x2y3 + 3x3y6 + 4xy
2. 5x7y5 – 2x2y4 + 7x4y2
3. 12x4y2 – y5 + 3x + 8x6y3
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
POLYNOMIALS
1. Write in descending order: 8, 16, 2, 6, 21, 0
2. Write in descending order:
1. 2x3 + 3x5 + 4x
2. 5x2 – 6x4 + 2x3
3. 23x8 + 14x5 – 34x2
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
POLYNOMIALS
 Put these in descending order according to the X value
1. 2x2y3 + 3x3y6 + 4xy
2. 5x7y5 – 2x2y4 + 7x4y2
3. 12x4y2 – y5 + 3x + 8x6y3
POLYNOMIALS
1.
2.
3.
4.
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:
a) 2x + 3x2 – 7
b) 7xy2 – 5x3y + 2y4