(2x%5E3%2B4x%5E2-5)-multiply.jpeg "(3x-1)(2x^3+4x^2-5) Multiply")
Multiplying Polynomials: (3x - 1)(2x³ + 4x² - 5)
This article will guide you through the process of multiplying the two polynomials, (3x - 1) and (2x³ + 4x² - 5).
Understanding the Process
Multiplying polynomials involves distributing each term of one polynomial to every term of the other polynomial. This process is often referred to as the FOIL method when dealing with binomials, but the principle remains the same for any number of terms.
Step-by-Step Multiplication
-
Distribute the first term of the first polynomial:
(3x) * (2x³ + 4x² - 5) = 6x⁴ + 12x³ - 15x
-
Distribute the second term of the first polynomial:
(-1) * (2x³ + 4x² - 5) = -2x³ - 4x² + 5
-
Combine the results:
6x⁴ + 12x³ - 15x - 2x³ - 4x² + 5
-
Simplify by combining like terms:
6x⁴ + 10x³ - 4x² - 15x + 5
Final Result
Therefore, the product of (3x - 1) and (2x³ + 4x² - 5) is 6x⁴ + 10x³ - 4x² - 15x + 5.
Key Points to Remember
- Distribute carefully: Ensure that each term in one polynomial is multiplied by every term in the other.
- Combine like terms: This step simplifies the expression and presents the final answer in its standard form.
- Practice: Multiplying polynomials is a fundamental skill in algebra. Practice with various examples to improve your proficiency.