Unit 5
Rewriting a sum as a product. Factoring is the tool that turns an equation into a set of zeros, which is why it dominates the next unit.
Lesson 5.1
Multiply every term in one factor by every term in the other, then combine like terms. Squaring a sum creates a middle term; it is not the same as squaring each term separately. The product of conjugate binomials cancels the middle terms.
Lesson 5.2
Factoring reverses multiplication. Begin by finding the greatest common factor shared by all terms, including both numeric and variable factors. Dividing each term by that factor produces the remaining expression. Expand the result to verify the factorization.
Lesson 5.3
For a monic quadratic, seek two numbers whose product is the constant term and whose sum is the linear coefficient. When the leading coefficient is not 1, check both leading and constant products. A factorization is complete only after common factors and special products have been considered.
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