A review on polynomials, monomials, binomials, trinomials and etc. This is also a review on identifying the degree of a polynomial.

1. A REVIEW ON
POLYNOMIALS
Prepared by:
Ruby Rose Ann B. Panganod,LPT

2. WHAT IS A POLYNOMIAL?
- A polynomial is an algebraic expression
that represents a sum of one or more
terms containing whole number exponents
on the variables.

3. EXAMPLES:
• 7𝑥𝑦2
𝑧
• 9𝑥2
− 4𝑥 + 5
•10𝑥 + 9𝑦 − 3𝑧
• 3𝑦2
+ 2𝑥2

4. Are these polynomials?
•11𝑥2 − 46𝑥 − 5
• 6𝑥−1
+ 8𝑦 − 5
•
1
2𝑥
+ 5𝑥2
•13𝑥3
+ 18
POLYNOMIAL
NOT A POLYNOMIAL
NOT A POLYNOMIAL
POLYNOMIAL

5. Based on the number of
terms, polynomials can be
identified as monomial,
binomial and trinomial.

6. A polynomial with one term is called a
MONOMIAL.
A polynomial with three terms is called a
TRINOMIAL.
A polynomial with two terms is called a
BINOMIAL.

7. A polynomial with more than
three terms have no special
name.

8. EXAMPLES:
MONOMIAL BINOMIAL TRINOMIAL
9𝑥2
𝑦 9𝑥2
𝑦 − 5x 9𝑥2
𝑦 − 5x + 1
5𝑏3
5𝑏3
+14𝑏2
5𝑏3
+14𝑏2
− 21𝑏
−16𝑥 −16𝑥 + 28 −16𝑥 + 18𝑦 − 28
45 5𝑏3
+ 1 5𝑏3
+ 5𝑎3
− 8

9. Polynomials can also be
classified using their degree.

10. The degree of a monomial is the total
number of times its variables occur as
factors.
−5𝑎𝑏2
𝑐3
EXAMPLE:
The degree is 1+2+3 = 6

11. The degree of a polynomial is the
greatest of the degrees of its terms.
𝑎2
𝑏 + 𝑎2
𝑏2
− 𝑎𝑏
EXAMPLE:
The degree of 𝑎2
𝑏 is 3. The degree of 𝑎2
𝑏2
is
4. The degree of 𝑎𝑏 is 2. Therefore, the degree
of 𝑎2
𝑏 + 𝑎2
𝑏2
− 𝑎𝑏 is 4.

12. Like terms are terms that contains
the same VARIABLES and
EXPONENTS. If the terms differ by
at least one variable, they are
called Unlike terms.

13. EXAMPLES:
LIKE TERMS UNLIKE TERMS
4𝑥 𝑎𝑛𝑑 7𝑥 4𝑥 𝑎𝑛𝑑 3𝑦
5𝑏3
and 2𝑏3
−9𝑥3
and 14𝑥2
−16𝑦 𝑎𝑛𝑑 4𝑦 −16𝑥 𝑎𝑛𝑑 − 1
4𝑎2
𝑏 𝑎𝑛𝑑 5𝑎2
𝑏 5𝑎2
𝑏 𝑎𝑛𝑑 4𝑎𝑏2

14. QUIZ

15. A. Give 3 examples of the ff:
1. Monomial
2. Binomial
3. Trinomial

16. B. Tell whether each expression is a
polynomial or not.
1.
1
𝑥
2. 11 + 2𝑦
3. −25𝑥3
𝑦2
𝑧
4. 25𝑥−3 𝑦2 𝑧
5.
1
𝑥−2

17. C. Give the degree of each polynomial.
1. −5𝑥 − 10𝑥2
2. 15𝑥
3. 5𝑥8
𝑦2
𝑧
4. 25𝑥3
𝑦2
𝑧 + 25𝑥3
𝑦𝑧2
− 𝑦10
5. 2𝑚𝑛3
− 4𝑚5
𝑛

18. D. Simplify by combining like terms.
1. 4𝑎 + 5𝑏 − 6𝑎 + 7𝑏
2. 5𝑥 + 9 − 6𝑥 + 7 + 4𝑦
3. 5𝑥3
+ 2𝑦2
+ 4𝑧 − 5𝑥3
− 4𝑦2
− 6𝑧
4. 6𝑦2
− 2𝑦2
+ 8𝑦2
− 10𝑦2
5. 4𝑥 − 8𝑦 + (5𝑥 + 2𝑦)