we've all been there where we had to go ahead and factor a trinomial where the leading coefficient is not one and here's a way that you may not have learned in school especially if you want to score in the U.S that's going to help you that's very trinomial where the leading coefficient is not one here we go first take that 12 multiply to the six so we'll go through 12 times 6 and the expression becomes x squared plus 17x plus 72. next we're just going to go ahead and Factor this to factor this we have X Plus and X Plus and to find out the two numbers that goes in here we need to find two numbers that multiplies to 72 and adds up to 17. first of all the list of numbers that multiplies to 72 are 1 and 72 2 and 36 3 and 24 4 and 18 6 and 12 and 8 and 9. then all these pairs of numbers that we have what two numbers as of 17. eight and nine so I'm going to put 8 here and I'm going to put a 9 here next you know that 12 that we multiply where did it go well we multiply by 12 so we're going to divide it by 12 here then once we reduce the fractions it becomes X plus 2 over 3 and X plus three over four to complete all we have to do is take the denominator multiply to the X take the 3 multiply to the X giving us 3x Plus 2. next we're going to take that 4 multiply to the X giving us 4X Plus three and of course if you multiply this out you'll get 12x squared plus 17x plus 6. or factoring the original expression that would be our final answer let me do another example here's a second example just as in the first example I'm going to take the leading coefficient of 6 multiply to the C value where we get x squared minus 5X minus 24. next we're going to factor this thing and again we get the X in the front however because this is negative the third term it's going to be plus minus again whatever the third term is negative we get 1 plus and 1 minus again we need to find two numbers that multiplies to 24 first which are 1 and 24 to a 12 3 and 8 4 and 6. and this time instead of adding because the two signs that are opposite of each other we want to find two numbers where we subtract and get five and it's going to be three and eight because eight minus three of course is five only thing you have to figure out is does the eight go here or the 8 goes here since that's negative 5 we want to put the bigger number with the negative so we put the eight here and the other number or the three goes right there next you'll have six that we multiply I'm going to divide the 3 and the eight by six and by reducing the three over six and the eight over six we get X plus one half and x minus four over three we're going to take that 2 multiply to the X giving us 2x Plus 1. notice the one stays the 2 is gone since we've tacked it out to the x again we're going to take that three tack it on to the x or multiply where we get 3x minus 4. again if you multiply this out you'll get 6X squared minus 5x minus 4. or if you factor the original expression the trinomial once again we get 2x plus 1 3x minus 4. so I hope this method if you haven't seen it before will help you back through trinomials with the leading coefficient of this band one as always thank you very much for watching my videos and supporting if you haven't subscribed please do so and give it a thumbs up