Exponents and Polynomials: Factoring a quadratic in two variables with leading coefficient 1 Factor x2 - 11xy - 12y2 where x is squared and 12y is squared

Here's how to factor the quadratic expression x² - 11xy - 12y²: **1. Find the Factors of the Coefficient on the y² term:** * The coefficient on the y² term is -12. Find two numbers that multiply to -12 and add up to the coefficient on the xy term (-11). * The numbers 1 and -12 satisfy this condition: (1)(-12) = -12 and (1) + (-12) = -11 **2. Rewrite the Expression:** * Replace the -11xy term with the two terms using the factors we just found: x² - 11xy - 12y² = x² + xy - 12xy - 12y² **3. Factor by Grouping:** * Factor out a common factor from the first two terms and a common factor from the last two terms: x(x + y) - 12y(x + y) * Notice how now (x + y) has become a common factor. **4. Factor out the Common Factor:** (x + y)(x - 12y) **Therefore, the factored expression is (x + y)(x - 12y)**