How many different ways can you factor a trinomial? This is intended as a tutorial for teachers to watch. Watch as a slideshow with animations, and it is much easier to follow. I recommend teaching your students 2 ways maximum. Otherwise I think it would be more confusing than helpful. Once you decide, alter the PowerPoint to meet your needs.  Happy Teaching!

The X (Magic-X, Big-X, Amazing-X, X-marks the spot) Whatever you want to call it… This will, by itself, factor a trinomial when A=1… <Then you just add steps when A≠1> Students should understand standard form Ax2+Bx+C A•C Attic& ceiling are up These two numbers must multiply to make A•C and add to make B CHECK SIGNS! x2-3x-10 a•c Both ( ) will start with x, Then use the two side numbers to fill in. 10 ● +2 -5 + -3 b ( ) ( ) x+2 x-5 B Basement is down

Way 1: The Advanced X This seems to be the method of choice for many of the high school teachers because then you only have to teach method and it covers all cases! I am including several examples of this method. Bring down the “A” term to both sides, but without the ”2” y2-3y-4 a•c Treat each as a fraction and reduce. -4 1y 1y 1 -4 -3 b Turn the “fractions” into factors Here is your answer! (y-4) (y+1)

Way 1: The Advanced X 15y2-16y+1 (y-1) (15y-1) 15y 15y Bring down the “A” term to both sides, but without the ”2” 15y2-16y+1 a•c Treat each as a fraction and reduce. 15 15y 15y -1 -15 -16 b Turn the “fractions” into factors Here is your answer! (y-1) (15y-1)

Way 1: The Advanced X 15y2-40y+25 5(3y2-8y+5) 5 (3y-5) (y-1) 3y 3y Factor first- if you can 15y2-40y+25 Bring down the “A” term to both sides, but without the ”2” 5(3y2-8y+5) a•c Treat each as a fraction and reduce. 15 3y 3y -3 -5 -8 b Turn the “fractions” into factors Here is your answer! 5 (3y-5) (y-1) Don’t forget the factor you pulled out!

Move factors over to box Way 2: The X-Box Move factors over to box 15y2-16y+1 15y -1 1 15y2 a•c Factor across y 15 -15y -15 y -1y -1 y -16 -1 Factor across b Factor up Factor up ( ) ( ) y -1 15y -1

Way 3: X, then ladder (elephant ears) Down on the left Factor out Up on the right 15y2-16y+1 15y2 +1 15y a•c 15 This is what’s left y -1 -15y -1y -15 y -1 y Factor out -16 b -1 This is what’s left Move the factors over to the ladders y -1 ( ) ( ) y -1 15y -1

Way 4: X, then group 15y2-16y+1 15y2 +1 -15y -1y 15y (y-1) + -1 (y-1) a•c 15 -15y -1y -15 y -1 y Move factors, then group them. -16 b Pull out common factors from each group Use “reverse” distribution 15y (y-1) + -1 (y-1) (y-1) (15y-1)

Way 5: X, then divide 15y2-16y+1 (15y-15) (15y-1) 15 (y-1) (15y-1) Group factors- move them over. If either group can be divided, do so. 15y2-16y+1 a•c (15y-15) (15y-1) 15 -1 -15 15 -16 This is what’s left. b (y-1) (15y-1)

Way 5: X, then divide- example 2 (oops, I should have factored first, but didn’t!) Group factors- move them over. If either group can be divided, do so. 3x2+9x-12 If both groups can be divided by the same thing, it goes in front. a•c (3x-3) (3x+12) 36 12 -3 3 3 9 b 3 (x-1) (x+4) This is what’s left.