Multiplication of Polynomials
Multiplying polynomials involves distributing each term of one polynomial to every term of the other polynomial. This process is called the distributive property. After distributing, you combine like terms (if any) to simplify the expression.
Steps for Multiplying Polynomials
- Distribute: Multiply each term in the first polynomial by each term in the second polynomial.
- Combine Like Terms: After distributing, Add together any like terms (terms with the same variable raised to the same power).
- Simplify: Write the final simplified polynomial.
Example 1: Multiplying a Monomial by a Polynomial
Problem: \( 3x(2x^2 + 5x - 4) \)
Solution:
Example 2: Multiplying Binomials (FOIL Method)
Problem: \( (x + 3)(x - 2) \)
Solution:
Example 3: Multiplying Polynomials (Trinomial by Binomial)
Problem: \( (2x^2 + 3x + 1)(x - 4) \)
Solution:
Key Points to Remember:
- Always multiply each term in one polynomial by each term in the other polynomial.
- Combining like terms is crucial for simplifying the expression.
- The degree of the resulting polynomial will be the sum of the degrees of the terms you are multiplying.