Factor by any method. See Examples 1–7. x²+xy-5x-5y

Verified step by step guidance

1. Group the terms in pairs to make factoring easier: \((x^2 + xy) - (5x + 5y)\).
2. Factor out the greatest common factor (GCF) from each group: \(x(x + y) - 5(x + y)\).
3. Notice that both terms contain the common binomial factor \((x + y)\).
4. Factor out the common binomial \((x + y)\): \((x + y)(x - 5)\).
5. The expression is now factored completely as \((x + y)(x - 5)\).

Key Concepts

Factoring by Grouping

Factoring by grouping involves rearranging and grouping terms in a polynomial to find common factors within each group. This method is useful when a polynomial has four terms, allowing you to factor out common binomials and simplify the expression.

Common Factors

Identifying common factors means finding terms or expressions that appear in multiple parts of a polynomial. Extracting these common factors simplifies the polynomial and is a crucial step in factoring complex expressions.

Polynomial Terms and Variables

Understanding polynomial terms and variables is essential for factoring. Each term consists of coefficients and variables raised to powers, and recognizing how these combine helps in grouping and factoring the expression correctly.