How Do You Reverse Foil?

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.

1. 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.

2. 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.

3. 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

4. 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)

5. Factor each pair

Factor each pair by finding the common factors. For example: 3x(2x + 5) + 2(2x + 5)

6. 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).

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