How Do You Factor Polynomials By Grouping?
Polynomials are algebraic expressions with at least four terms. Students can factor, or break down, these expressions into multiple expressions of three or fewer terms. Let’s look at the example: xy + 3y – 2x -6 Re-arrange the terms in the expression so that two consecutive terms have a common factor:xy + 3y – 2x – 6 = xy – 2x + 3y – 6Note that the order of (-2x) and (3y) is switched. Now find the common factor of each of the two consecutive terms:xy – 2x + 3y – 6 = x(y-2) + 3(y-2) Now group the common factors:xy – 2x + 3y – 6 = x(y-2) + 3(y-2) = (x + 3)(y – 2) Here’s an example of how to factor a polynomial expression with exponents:x^3 – xy^2 – x^2y + y^3 Re-arrange the terms in the expression so that two consecutive terms have a common factor:x^3 – xy^2 – x^2y + y^3 = x^3 – x^2y – xy^2 + y^3Note that the order of (- x^2y) and (- xy^2) is switched. Now find the common factor of each of the two consecutive terms:x^3 – x^2y – xy^2 + y^3 = x^2(x – y) – y^2(x – y) Now group the common fa
