Explain how to factor trinomials. Is there more than one way to factor trinomials? Show your answer using both words and mathematical notation. Give a problem to the class to try.

The way I factor trinomials is by taking the leading and the last term and multiplying them together. I then take the new number that those multiplied out to and figure out what two factors of that multiplied number can equal the middle number. For instance in the following trinomial 10x^2 -11x + 3. First we take and multiply the leading term, 10 by the trailing term, 3. This gives us 30. We much now factor 30 and find out which two factors of 30 when added together equal the middle term, 11. In the number 30 the factors are 1,2,3,5,6,10,15,30. Right off the bat I can see that 5 and 6 both add up to 11 and multiply to 30. Now our problem is that 5 and 6 do not add up to negative 11 so they must both be negative. So our new polynomial is, 10x^2 -5x -6x +3. To factor these you must now group and pull out the highest common factor from each problem. It is very simple! In order to factor this polynomial we have to pull a 5x out of the first grouping (10x^2-5x) (10x^2-5x) (-6x + 3) 5x(2x-1) -3(2x-1) (5x-3) (2x-1) x = 1/2 , or 3/5