1. A fun way to factor quadratics!

2.  You start by identifying the a, b and c values in your quadratic expression or equation.  Remember the form is ax 2 +bx+c  You may want to write down the values next to your problem.

3.  The board looks like a regular tic-tac-toe board.  You will place numbers in specific spots to properly factor your problem

4. ab a·c

5. 176 a=1 b=7 c = 6 a⋅c = 6 Fill in the boxes like this aba⋅c

6.  You have to find the factors of a⋅c that add up to b.  So, the factors of 6 are 1⋅6 and 2⋅3 where 1+6=7 and 2+3+5  Since b = 7, you would choose 1 and 6 and put them in the boxes under the 6 (it doesn’t matter which order).

7. 176 1 6 Factors of 6 That add to 7

8.  You have to find the GCF (greatest common factor) of the numbers in these boxes And put it here 176 1 16

9.  All that’s left is to multiply and get your answer. 176 111 166 X = X = Multiply... X Follow the arrows and fill in the blanks

10.  Now all you have to do is group some numbers to form the binomials.  The variables go with the numbers in the left column. Rewrite the circled numbers in binomial form like this… (x+6)(x+1)*  *You don’t usually see the 1 in front of the variable so you don’t have to put it there. 176 111 166

11.  with the factoring part anyway.  If you want to make sure your answer is correct multiply the two binomials to check, you should get your original trinomial. (x+ 6)(x+ 1) = x 2 + 7x + 6

12.  You may have to take this one step further and find the zeros of your quadratic equations, but you won’t have to do that unless the directions tell you to solve or find the solutions.  If you do need to solve…(next slide, please)

13.  Use the zero product property and set each binomial equal to zero and solve for the variable.  x+1=0x+6=0 -1 -1 -6 -6 x =-1 x=-6  The solutions are -1 and -6 (where the parabola intercepts the x-axis)