for reference only

1. Polynomial
→ refers to an expression consisting of variables (also called
indeterminates), coefficients, and operations of addition, subtraction,
multiplication, and non-negative integer exponents.
→ essentially means "many terms."
The word polynomial is derived from two parts:
Poly: from the Greek word polys meaning “many”
Nomial: from the Latin word "nomen", meaning "term."

2. Polynomials can be classified into different types
based on their characteristics
1. Based on the Number of Terms
Monomial: a polynomial with one term
ex. 3x2
, 7, −5y etc.
Binomial : two terms
ex. x+5, 3x2
−2x
Trinomial : three terms
ex. x2
+2x+1, 4a3
+3a2
−6
Multinomial: more than three terms
ex. x4
−3x3
+2x2
+x+6

3. •Addition: Combine like terms.
Ex: 3x2
+ 2x + 5 + x2
+ 4x −7 = 4x2
+ 6x − 2.
•Subtraction: Subtract coefficients of like terms.
Ex: 5x3
− 3x2
+ 4x − 1 −(2x3
+ x2
− 5x + 6) = 3x3
− 4x2
+ 9x − 7
•Multiplication: Use the distributive property.
Ex: (x + 2) (x2
− x + 3) = x3
+ x2
+ x + 6.
•Division: Use polynomial long division.
Ex : (x3
+ 2x2
− 5x − 6) ÷ (x − 2) = x2
+4x+3.

4. 2. Based on the Degree (Highest Power of the Variable)
•Constant Polynomial: Degree 0. It contains only a constant.
Example: 5,−35, -35,−3
•Linear Polynomial: Degree 1.
Ex: x+2, 3y−7x + 2,
•Quadratic Polynomial: Degree 2.
Ex: x2
+3x+2,4a2
−7a+1
•Cubic Polynomial: Degree 3.
Ex: x3
−2x2
+x−5, 4a2
−7a+1
•Quartic Polynomial: Degree 4.
Ex: x4
−x3
+2x2
−5x+1
•Quintic Polynomial: Degree 5.
Ex: x5
−3x4
+x3
−7
•Higher-Degree Polynomials: Degree 6 or more.
Ex: x6
+2x5
−x4
+4x−3

5. A linear polynomial (or linear function) can be represented as
a straight line on a graph.
For example, P(x)=2x+1

6. Quadratic Polynomial / quadratic equation
A quadratic equation is generally expressed in the form:
ax2
+ bx + c = 0, where a,b, and c are constants and a≠0
Example: x2
− 3x − 4= 0
Solution: quadratic formula:

7. x2
− 3x − 4= 0
Vertex = (1.5, -6.25)
X=4
X=-1

8. A cubic polynomial is a polynomial of degree 3. It has the general form:
f(x) = ax3
+ bx2
+ cx + d
Ex. y = x3
– 6x2
+ 11x – 6; let the (roots) or x= 1, x= 2, x= 3