the factoring unit included factoring by removing a common factor (monomial/binomial/grouping), factoring a trio Miao (inspection), and factoring the differences of squares. This unit works on writing the sums or differences of monomials as a product of polynomials… which is called factoring. There are three major types of factoring: removing a common factor, trinomial, or factoring the difference of squares.

Factoring by removing the GCF uses prime factorization which we studied in the number unit. You take out all the prime factors until you can’t any longer, pick the factors that appear in both/all of the whole numbers you’re factoring, using the lowest possible exponent from those that are there, and multiply them together. Which would look like this for finding the GCF of 48 and 72… which equals , and which equals the common numbers are 2,3 with the lowest exponents of both being , then multiplying them together gets you 24. Now with factoring by removing the GCF, you remove the GCF and write it separate from the leftover polynomial.

Factoring a trinomial in the form generally involves inspection, which is where we find two integers which have a product equal to c, and a sum equal to b. If no two such integers exist then the polynomial cannot be factored. *remember that if the product is negative, then one integer must be positive and one negative, and if the product is positive, they both must be positive or negative. Factoring by inspection looks like so…

Factoring the difference in squares is used for binomials that are written in the identity and the variables can be replaced by numbers, variables, monomials, or polynomials. Factoring he difference of squares ends up looking like this and can be verified by expanding the product of the factors.