Factoring Polynomials Factoring by Decomposition We are going to start today with the second easiest form of factoring (the easiest being factoring out the GCF). All of the polynomials that we will be factoring today will be quadratic (or quadratic form), mostly trinomials. Some, towards the end, aren’t polynomials, but we will still be able to factor them. Also, most of them will start with x2. There will be some special cases where the x2 has a coefficient other than one, but we are going to save the bulk of that type until day 2 of factoring. Factoring mainly requires an understanding of how polynomial multiplication works and logic. We are basically going to reason our way through this process.

Factoring Polynomials: Type 2: Quadratic Trinomials with a Leading coefficient = 1

Factoring Polynomials: Type 2: Quadratic Trinomials with a Leading coefficient = 1 Factoring by Decomposition Multiply a and c Look for two numbers that multiply to that product and add to b Break down the middle term into two terms using those two numbers Find the common factor for the first pair and factor it out & then find the common factor for the second pair and factor it out. From the two new terms, place the common factor in one bracket and the factored out factors in the other bracket.

Factoring Polynomials: Type 2: Quadratic Trinomials with a Leading coefficient = 1 Factoring by Decomposition Multiply a and c Look for two numbers that multiply to that product and add to b Break down the middle term into two terms using those two numbers Find the common factor for the first pair and factor it out & then find the common factor for the second pair and factor it out. From the two new terms, place the common factor in one bracket and the factored out factors in the other bracket. The 2 nos. are -20 & 1