Multiply: (2x−5)(x²−3x−6). (Section 5.2, Example 3)

Key Concepts

Polynomial Multiplication

Polynomial multiplication involves distributing each term in one polynomial to every term in another polynomial. This process is often executed using the distributive property, which ensures that all combinations of terms are accounted for. For example, in multiplying (2x−5) by (x²−3x−6), each term in the first polynomial must be multiplied by each term in the second.

FOIL Method

The FOIL method is a specific technique used for multiplying two binomials, standing for First, Outside, Inside, Last. While the given expression is not strictly two binomials, understanding FOIL helps in organizing the multiplication process. It emphasizes the importance of systematically combining terms to avoid errors, particularly in larger polynomials.

Combining Like Terms

Combining like terms is the process of simplifying an expression by adding or subtracting terms that have the same variable raised to the same power. After multiplying polynomials, the resulting expression often contains multiple terms that can be simplified. For instance, in the product of (2x−5)(x²−3x−6), after distribution, terms like x² and -3x can be combined to streamline the final expression.