Reverse FOIL (first, inner, outer, last) is another way of saying factorization by grouping. To factor a polynomial, find the product of the first and the last coefficients. Then, find the two factors of the product that add up to the middle coefficient. Split the middle term into two terms, and then group the terms into two pairs. Factor each pair.
- Find the product
Find the product of the first and the last coefficients. Polynomials are written: ax^2 + bx + c, where "x" is the variable, and "a," "b" and "c" represent coefficients. To find the product, multiply "a" and "c" together. For example: 6x^2 + 19x + 10, where a = 6, c = 10 and 6 x 10 = 60.
- Find two factors of the product
Find two factors of the result of "a" and "c" multiplied that add up to the center term "b." For example: 15 x 4 = 60 and 15 + 4 = 19.
- Rewrite the center term
Split the center term into two terms using the two factors. Use the proper signs, meaning positive and negative. To continue with the example: 6x^2 + 15x + 4x + 10
- Group the terms
Group the four terms to form two pairs. Pair the first two terms together and the last two terms together. For example: (6x^2 + 15x) + (4x +10)
- Factor each pair
Factor each pair by finding the common factors. For example: 3x(2x + 5) + 2(2x + 5)
- Factor out the binomial parentheses
Factor out the shared binomial parentheses. In the example, since both parts have (2x + 5) in common, the new equation reads: (3x + 2)(2x + 5).