Polynomial Operations
In this lesson, we will explore the operations you can perform on polynomials, including addition, subtraction, multiplication, and division. Polynomials are expressions consisting of variables and coefficients, involving terms in the form of anxn+an−1.
Example: Adding and Multiplying Polynomials
Let's consider two polynomials:
P(x)=3x2+2x+1
Q(x
Step 1: Addition of Polynomials
To add P(x) and Q(x), we combine like terms:
R(x)=P(x)+Q(x)
R(x)
Step 2: Multiplication of Polynomials
Now, let's multiply P(x) and Q(x):
S(x)=P(x)⋅Q(x)
S(x)
We will use the distributive property (FOIL method for binomials):
- 3x2⋅5x2=15x4
Now combine all terms:
S(x)=15x4+(12x
Key Questions
- What is the result of adding 2x3+3x2+4 and 5x?
Keywords
- Polynomial
- Addition
- Subtraction
- Multiplication
- Division