In Exercises 15–58, find each product. (x−1)(x+2)

Verified step by step guidance

1. Identify the expression to be multiplied: $(x-1)(x+2)$.
2. Apply the distributive property (also known as the FOIL method for binomials): First, multiply the first terms: $x\cdot x$.
3. Next, multiply the outer terms: $x\cdot 2$.
4. Then, multiply the inner terms: $-1\cdot x$.
5. Finally, multiply the last terms: $-1\cdot 2$.

Key Concepts

Polynomial Multiplication

Polynomial multiplication involves distributing each term in one polynomial to every term in another polynomial. In the case of (x−1)(x+2), you apply the distributive property, also known as the FOIL method for binomials, which stands for First, Outside, Inside, Last. This process helps in combining like terms to simplify the expression.

Like Terms

Like terms are terms that have the same variable raised to the same power. When simplifying polynomials, it is essential to combine like terms to reduce the expression to its simplest form. In the product of (x−1)(x+2), after distribution, you will encounter terms that can be combined, such as the x² term and the constant terms.

Standard Form of a Polynomial

The standard form of a polynomial is when the terms are arranged in descending order of their degree. For example, a polynomial like x² + x - 2 is in standard form. After finding the product of (x−1)(x+2), it is important to express the result in standard form for clarity and ease of further calculations.